(FORTUNE Magazine) – If you could build a CEO to specs, how would you do it? As a platform, you'd engineer someone with machine-like stamina--someone who could work 100 hours a week for 24 years with no apparent ill effects. You'd add intelligence enough to excel at the nation's best schools, vision enough to peer into the future and recognize the world's most promising business opportunities. You'd make him a discerning judge of talent, and you'd make him tough--able to push aside his own handpicked managers if they didn't deliver. He would budget his time with iron discipline: up at 5:30 daily for a cardio workout while reading the papers and watching CNBC, allocating 30% of his workweek to people evaluation, 30% to operations, 30% to growth initiatives, and 10% to governance, investor communications, and board communications. And since you could do whatever you want, you might as well engineer all of those extraordinary elements into a disarming package: tall (6-foot-4), good-looking, genial, relaxed, approachable.

Jeff Immelt is that wish-list CEO. The only thing missing is wish-list results. General Electric's CEO--the alpha male of the executive class, just ninth in a line of succession that began with Thomas Edison--is trying to solve one of the biggest problems any CEO now faces by pulling off one of the largest transformations any CEO has tried in years. (For a boss in an even tougher bind, see "Can One Man Save GM?") To get GE's terribly performing stock back on track, Immelt has to make this mammoth outfit grow faster. To do that he has to answer the largest questions shaping the world economy--which countries, which industries will grow fastest and biggest? And he has to get 320,000 employees--teammates, he always calls them--to follow his lead. Whether he succeeds or fails will influence the management of corporations worldwide and determine the future of the most widely owned company on the planet. Millions of people are betting hundreds of billions of dollars on his success.

Yet the guy is a mystery. Ask intimates what's most important about him, and you get a variant of the same answer: "He is exactly the person who you think he is when you meet him," says John Rice, whom Immelt recently made a GE vice chairman. Warren Buffett, a major fan, says, "He doesn't feel he has to dazzle anybody this month or this week." Fittingly, Immelt says of himself, calmly, "I'm direct and I'm truthful."

The lack of pretension or even tension is what everybody notices, but it leads you seriously astray in understanding the man, the way he works, and whether he's up to his considerable challenge. You might think, for example, that Immelt is easy to work for--not especially demanding. That's a mistake. He is brutally demanding, even by GE standards. He has repeatedly done something most CEOs find unbearably painful: taken executives out of high-level jobs he had put them into, and quickly. He promoted Yoshiaki Fujimori to head GE Plastics but less than two years later moved him out. He made longtime GE executive Gary Rogers a vice chairman--but in 2003 Rogers stepped down to be a "senior advisor" to the company until his retirement a year later. Says Jack Welch, who until now has not commented publicly on his successor: "He's a lot tougher than you might think, but it's beneath his affable manner. That's a combination that works."

The contrast between Immelt and Welch is striking but misleading. It's true they couldn't appear more different: The Big Easy vs. Mr. Tightly Wound. But Welch could just as enthusiastically hug a manager as chew him out, while Immelt appears to have ice water in his veins. He may well be tougher than the man once famed as one of America's toughest bosses. As Welch himself says, "At times I might get too emotional. He doesn't."

Immelt's ease could tempt you to infer that success has been a breeze--that maybe he doesn't apply himself terribly hard. That too would be wrong. FORTUNE 500 CEOs are an extraordinarily hard-working group, yet even in that elite universe Immelt qualifies as a hero of capitalist labor. Says his brother, Steve: "He works pretty hard at making it look easy. When we were kids he'd sneak away--to study." That was when they were growing up in Cincinnati, where their father was a 38-year GE employee, a middle manager in the aircraft-engine business. Even in high school, Jeff was busy--football, basketball, baseball, great grades. Today, says Steve, "it looks easy because he's working his butt off in a way you don't see."

Immelt, 49, says he's been working 100 hours a week for 24 years. That does not take him back to his 1978 graduation from Dartmouth, where he was football team captain (as offensive tackle) and a fraternity president who liked to party. Nor does it go as far back as his two-year stint marketing Duncan Hines brownie mix at Procter & Gamble, where he sat next to Steve Ballmer, now CEO of Microsoft. The future chiefs of the world's two most valuable companies played paper-wad basketball, "were incorrigible," says Immelt with a laugh, and "were never going to be employees of the month." The 24 years go back to his time at Harvard Business School, which Immelt says he approached like a job. The most valuable thing he learned there? "There are 24 hours in a day, and you can use all of them."

Most hard-charging types have put in a 100-hour week or two. But month after month, year after year--is that even possible? Let's do the math. If you worked from 7 A.M. to 9 P.M. seven days a week, you'd still be two hours short of 100 hours. If Immelt has been working that hard for 24 years, then he has already done 60 years' worth of 40-hour weeks. Around GE they say he has grown noticeably thinner and grayer since becoming CEO. Maybe the wonder is that it didn't happen sooner.

These days, after his early exercise routine, he heads to the office a few exits up the Merritt Parkway in Connecticut. He regularly reviews his calendar to check that he's allocating his time properly--evaluations, operations, growth, governance, communication. "I've always been extremely disciplined," he says. The day generally ends with a dinner for customers or employees. That's when he's at home. He spends about 60% of his time on the road, where the hours are at least as bad. Here he is on a recent swing through San Francisco: The first meeting is with institutional investors at 7 A.M. Then he addresses some 200 retail investors at 8:30, standing comfortably for 25 minutes with his left hand in his pocket and his right hand holding his PowerPoint remote; after his talk, he answers questions for an hour. Then it's more institutional investors, followed by GE salespeople in Burlingame, a presentation to customers, and finally a big reception for customers and top salespeople. He seems as energetic at the end of the day as at the beginning. He had run virtually the same routine in Los Angeles the day before. (Yes, his wife, Andrea, knew what she was getting into--they met when both worked at GE Plastics. Their only child, Sarah, heads off to Boston College this fall, but unlike most empty-nesters, Immelt won't wonder what to do with the extra time.) "You have to have real stamina," he says.

The truth is that an unflinchingly tough, remarkably hard-working boss is what GE badly needs. The company faces a problem--lousy stock performance--that sounds commonplace but in this case decidedly isn't. What's different at GE, making Immelt's situation unique and significant, is that the trouble and its solution are on a scale that most CEOs never contemplate. The size of the problem: Since Immelt was handed the keys on Sept. 7, 2001, GE stock is down 15% while the major market indexes are up 7% to 11%. That percentage gap is bad news but too abstract to convey the problem's magnitude. Think of it in dollars: If the stock had merely achieved mediocrity, matching the S&P 500 since Immelt's arrival, GE would be worth over $100 billion more than it is. For perspective, there are not 25 companies in America with a total market cap of $100 billion.

Now start thinking about a solution, and again Immelt must plot on a massive scale. To raise GE's stock price by $1, he must produce about $650 million of new, after-tax profits that would continue every year. Again, for perspective: At 300 of the FORTUNE 500 companies last year, total profits didn't reach $650 million. But GE must add that much just to raise the share price by a buck--and the shares are about $6 below where they were when Immelt took over. The fix: Immelt must find opportunities with global scale, since they're the only ones big enough to make a difference for GE. And he must think long term: As with Welch, the board expects him to be a 20-year CEO, and he knows that, barring disaster, he has 16 more years in the job.

Those perspectives lead him to large thoughts on the world's future. Developing economies will grow faster than developed ones, and Immelt believes their need for basic products and services--water, energy, transportation, health care, financing--will grow faster than their economies. For example, GE figures nearly half the world's people will soon be water-stressed--unable to get the clean water they need. That's a huge long-term opportunity, as are those other industries, so Immelt is making major investments in all of them.

Immelt doesn't worry about what could go wrong in the world as much as he worries about how to position GE for whatever happens. Thus, $65 oil is a problem for his plastics business because it's the main raw material, but it's an opportunity for jet engines, locomotives, and power systems because if GE can make those products more energy efficient, customers will love them. He's confident about most of the trends he's betting on, but he cites two overarching uncertainties--two things "that are going to be determined while I'm in this job that are bigger than GE. One is where health care goes in this country and on a global basis. That's going to be played out in the next ten or 15 years." How will the developed world pay for the health care of its rapidly aging population, and how will the developing world meet its people's fast-rising health-care expectations? The other major uncertainty is "the future of the U.S. as a manufacturing nation--that's going to be played out not in the next 50 or 100 years, but in the next ten or 15 years."

In line with his big-picture expectations, Immelt is recasting GE broadly and deeply. The most fundamental step is changing his portfolio of businesses. Many of his acquisitions have been individually small--a wind-energy business from the defunct Enron, Ionics in water purification--but Immelt is buying the opportunity for future growth. A few buys were quite large, notably Universal, the movie studio and theme-park business, which he combined with NBC. His biggest acquisition was Amersham, a British health-care outfit that he bought for $9.5 billion and combined with the GE unit that makes CT scanners and MRI machines. Those were his portfolio additions. His major divestitures were in GE's insurance business, which wasn't producing the returns on capital he wanted. So he sold parts of it (including one piece to Buffett's Berkshire Hathaway) and spun off other parts last year.

Today Immelt pretty much has the business portfolio he wants. That's the good news. The bad news is that he spent $60 billion on it--new capital invested in the business on which a return must be earned. Thus we reach another critical part of Immelt's strategy, the great growth push. Says Immelt: "We don't buy growth, we grow what we buy," and growing what he's bought is now his overwhelming imperative.

One way he's going after that goal: publicly reviving GE's scientific research labs, bestowing upon them vastly increased dollars and prestige. Immelt figures technology innovation is a key to growth for two reasons. First, virtually every product and service in today's markets is in danger of being commoditized. If GE scientists are on the leading edge of research into, say, nanotubes, as they are, then GE has a fair chance of creating products the competition can't match, at least for a while. Second, innovative products create the best opportunities for services, which are where GE's manufacturing busi- nesses earn their real money. For example, GE makes no money selling jet engines, but it makes a ton of money servicing and upgrading those engines over their 40-year lives. "The most valuable services in the world start with R&D and manufacturing," Immelt says. "Jet engines, gas turbines, MR scanners--you don't get any of that service revenue without the technology investment." That's why he's casting GE as a tech company, an identity it hasn't had in decades.

Fast growth is what drives Immelt's interest in developing economies. The opportunities are huge for many GE businesses. For example, the U.S. has one commercial aircraft for every 45,000 people, but China has only one per 1.6 million people, and India one per six million; as these economies develop, their demand for jet engines will be vast. They will need electric-generating capacity on an enormous scale. They will be improving the quality of their water and their health care, and doing it for billions of people. Their consumers and businesses will need financial services.

That's heady stuff, but Immelt is thinking much bigger. He realizes that while other companies can compete in any of those businesses, only GE can compete in all of them, and they all involve purchases that are government-made or government-approved. So GE's customers will increasingly be nations with which the company will be, literally, partners in economic growth. You need electricity? We can provide all the equipment. Don't forget you'll also need locomotives to haul more coal from the ports; we can sell you those. Your new electricity will be powering new factories with a tremendous demand for clean water, which we can make sure you get. You'll need bigger airlines to handle all that commerce--we can sell you the jet engines and, for that matter, lease you the airplanes. And of course you can finance everything through us.

The vision is grand but apparently realistic. Revenues from the developing world were up 37% last year, to $21 billion. Immelt says the company has won 70% of China's gas turbine orders over the past two years, and it has won a commitment for 80 locomotives plus control equipment. In Qatar, says Immelt, GE is getting a big chunk of a major pipeline project, plus a $2 billion order from Qatar Airways, plus major water-desalination projects, plus extensive service and training contracts; the target is $10 billion of revenue by 2010. Nicholas Heymann of Prudential Securities, the top-ranked GE analyst, figures 40% of GE's total revenue growth over the next five years will come from developing countries.

Immelt's growth strategy has another feature that says a lot about him. He decided to make GE's marketing as great as its vaunted finance and human resources operations. "At first no one knew what he was talking about," says vice chairman Dave Calhoun. It's not that GE hated customers; it just wasn't customer-centric. "Marketing had become a lost function during the 1990s," says Immelt, so restoring it was a fat opportunity to make GE more competitive. To him it's the basis of an important change in the GE culture, making it more externally focused, measuring GE's success by customers' success. If it works, the change will be significant. As he puts it, "The purpose of this generation of GE leaders is to make the company as good externally and commercially as it has always been operationally and financially."

Immelt is committed to his strategy. Can he execute it? That's rarely a problem at GE, where the disciplines of execution are at the heart of the culture. The biggest challenge through the rough patch of the past few years has been keeping and motivating the very best GE managers. Immelt was pumping up 625 of them this past January at an annual rite that brings them to Boca Raton each year. As usual, he opened with pointed jokes (one of his Top Ten Reasons 2005 Will Be a Great Year for GE: "We've replaced Father of the Pride with a test pattern," a jab at one of NBC's many flops). Then, to the team on whom he relies to carry his strategy, he put up a slide with a surprising tone: "If you didn't leave the last three years, you would be crazy to leave now!" The slide got a big laugh, as intended, because like all good laugh lines, it contained truth. Imploring people to stay? At GE? Yes, when those hard-charging managers are holding loads of underwater stock options.

But step back and look at the very big GE picture --Immelt's character, methods, strategy, and recent results--and you have to conclude the man is equal to his plan. He is changing what he wants to change. And the plan does make sense. In fact, you don't find many doubters; the closest you come are those who say it isn't paying off yet. Even that may be changing. Earnings per share in the past three quarters grew 13%, 19%, and 22%, a huge improvement over the recent past and well ahead of his goal. If he can keep growth anywhere near that, GE's multiple will improve and the stock will do what it's supposed to.

In any case, expect Immelt to just keep doing what he's doing. "He's a marathon runner," says Ram Charan, a consultant who has worked for Immelt and many other CEOs. He notes the Street was none too kind to Welch when he was reordering GE in his first few years as chief. Warren Buffett says, "Over the long run, which he has, the stock will behave itself." Buffett actually expects far more than that from Immelt: "He is likely to be the most respected spokesman for American business during the time of his tenure."

A world that got to know Welch very well is taking a while to figure out Immelt, who seems strikingly different from his predecessor but turns out to be a lot like him. Immelt's apparent serenity masks rigor, toughness, and a white-hot desire to win. He's quietly confident in what he's doing, but he won't rest--he can't--until he has proven that his deep redirection of one of the world's great companies is actually working. And of course he won't rest even then.