(FORTUNE Magazine) – When Coca-Cola revealed at the close of business on Monday, September 8, that Chairman and CEO Roberto Goizueta has lung cancer, the reaction on Wall Street signaled a sober reality: It's okay for America's most highly regarded CEO to step aside.

It sounds harsh to say, but Goizueta's work is essentially complete. In the 16 years since this virtually unknown and strikingly uncharismatic executive strode onto the scene as CEO (and thus steward of one of the world's most powerful brands ever), he reformulated a business that was actually floundering--organizationally, culturally, and financially. Against all expectations, he turned Coke into America's most admired company, according to FORTUNE's surveys. And he transformed himself as well. A patrician Cuban immigrant displaced by Castro's revolution, he was practically penniless when he moved to America 37 years ago. Working for only one company and building his wealth with the stock of Coca-Cola alone, he became a billionaire.

As strategist, global spokesman, and the soul of what the Coca-Cola Co. has become under his rule, he seemed indispensable. And since he is a proud and very stubborn man, Goizueta always believed this to be true. As early as 1993, FORTUNE declared unequivocally that Doug Ivester, Coke's little-known financial wizard, would be the next chief executive. But Goizueta has never anointed him publicly. He has praised him, but he has also hinted that Ivester has room to grow. Three years ago the Coke board (which means three directors in particular--Warren Buffett, Herbert Allen, and SunTrust Banks CEO Jimmy Williams) asked Goizueta to stay on indefinitely. And so it was no surprise that last November, when he turned 65, Coke's customary retirement age, Goizueta had every intention of carrying on.

Of course, no one on this Earth--least of all FORTUNE--knows for sure how Goizueta's illness will play out. Coke says that he is undergoing radiation and chemotherapy, and that he has no plans to step down, even temporarily. But it's fair to say that the disclosure of his cancer brings into sharp relief the discussion of his succession, which had actually been on the tom-toms within the company for at least a year--and getting louder lately.

Just a couple of weeks before Goizueta's cancer was discovered, the betting inside Atlanta headquarters was that he planned to announce Ivester's promotion to CEO at a meeting of Coke's worldwide bottlers in Monaco. Again, though, nothing happened. Coke says there never was such a plan--no one close to Goizueta has so much as hinted that he has ever seriously charted his abdication. But some speculate the plan existed and was derailed because Coke's stock--always Goizueta's focus--had gotten walloped recently by worries over upcoming earnings shortfalls.

A courtly gentleman who almost always has a True cigarette in his hand and has not been a regular visitor to doctors' offices, Goizueta learned of the cancer shortly after returning from the Monaco meeting. In the office that week he felt unusually fatigued. On Saturday morning he checked into Emory University Hospital for tests, and the doctors there found a malignant tumor on his right lung. When Coke disclosed the news--using the term "localized lung tumor" and noticeably avoiding the word "cancer" in its press release--the market hardly reacted at all. Coke's shares fell less than a dollar.

Goizueta was still in the hospital at the time FORTUNE went to press, though he was scheduled to go home soon. Inside his hospital room, a suite originally designed for former Coke CEO Robert Woodruff, Goizueta is reportedly maintaining his resolute workaholism. He has had an ILX machine installed to quench his desire for constant stock-price updates. Two fax machines deliver memos from the office along with get-well greetings from employees and friends around the world.

Upon first speaking with Ivester in his hospital suite, Goizueta told him: "It's all right if people want to worry about me. But they shouldn't worry about the company, because it's in better shape than it's ever been."

It is indeed a tribute to Goizueta that succession at Coca-Cola is, to Wall Street at least, no big deal. The consummate long-term strategist, he planned well. Ivester has been Coca-Cola's virtual CEO since 1994, when Goizueta appointed him president and chief operating officer. For the past three years the two men have had an almost perfect partnership--Ivester managing the business (Coke's five geographic presidents and the head of global marketing report to him) and Goizueta managing big-picture strategy and Coke's marvelous relationship with the Street. "The transition will be seamless," says Morgan Stanley Dean Witter analyst Andrew Conway, who had lunch with Goizueta at Coke headquarters a few days before he was hospitalized.

To get a fix on Ivester, 50, and where Coke goes from here, you need to understand Ivester's mentor and role model, Roberto Goizueta. At first glance, the two men seem nothing alike--the Latin immigrant and the native Georgian. One learned English as a second language; the other speaks only Southern drawl. Goizueta is a chemical engineer by training; Ivester is an accountant. In manner, Goizueta is elegant and aristocratic, while Ivester is homespun and plainspoken.

Beneath the surfaces of these two men, though, their similarities are striking. Goizueta and Ivester both rose to great success from obscurity. Early on, they were underestimated by colleagues, and by themselves as well. Intensely growth-minded, they have had highly disciplined approaches to managing their businesses and their careers. "Doug is the hardest-working man I've ever met," Goizueta says. And they share a wisdom about what makes a company great: a monomaniacal focus on building investor wealth.

The son of a sugar plantation owner, Goizueta was educated in America--boarding school, then Yale University--and started his career in Coke's technical department in Havana in 1954. He figures that if Castro hadn't seized power, he might still be working in Cuba today as an owner of a Coke bottling plant. Instead, Goizueta and his wife, Olguita, escaped in 1960, leaving their wealth and security behind. They landed by boat in Florida with just $40 and 100 shares of Coca-Cola stock. (Those 100 shares, which he kept, are now worth more than $3 million.)

As a Coke manager, Goizueta moved almost unnoticed through the bowels of the company in various technical and administrative jobs; he never even ran a business until he became CEO. In 1981 he won the top job in a particularly patrimonial way: He had befriended legendary former CEO Woodruff. And at 91, Woodruff, who was officially chairman of the board's finance committee but was known inside as The Boss, still controlled the company. Woodruff was so impressed with Goizueta's quiet intellect and integrity that he persuaded the board to veto a candidate favored by J. Paul Austin, Coke's then-CEO, who, unknown to the public, was suffering from Alzheimer's disease.

Back then Coca-Cola was a muddle of businesses--wine, coffee, industrial water treatment, and shrimp farming, as well as soft drinks. Ever the technician, Goizueta analyzed each component according to a basic financial formula and concluded that all but one reduced shareholder value. The Goizueta Rule of Investment: "You borrow money at a certain rate and invest it at a higher rate and pocket the difference. It's simple." Before anyone else, he was promoting "economic profit" (after-tax operating profits in excess of capital costs) and marketing it to Wall Street in personal letters that he habitually writes to analysts. "Economic profit," well-known today as EVA (economic value added), is a favorite tool for increasing shareholder wealth.

Unlike other celebrity CEOs--Welch, Gates, Grove, the late Sam Walton--Goizueta's managing style was always more cerebral than hands-on. He has tended to visit a half-dozen countries a year (Coke earns 80% of its profits abroad). But his favorite perch is behind his mahogany desk on the 25th floor of Coke's headquarters. There he has defined, as he says, "the character of the company."

In fact, what he did--together with his longtime president, Donald Keough, now chairman of Allen & Co.--was completely make over the character of Coca-Cola. It used to be terribly conservative. For example, the company never borrowed a dime before 1980. Goizueta borrowed billions to buy independent bottling fiefdoms around the world and upgrade their distribution systems. And he encouraged risk taking: While his CEO predecessors prohibited putting the Coke trademark on any new product, Goizueta brought out Diet Coke in 1982. It was the most successful consumer-product launch of the '80s.

He veered out of beverages just once, when he bought Columbia Pictures for $692 million in 1982. As a movie studio Columbia was a bust--remember Ishtar?--but Goizueta sold out to Sony in 1989 for $1.5 billion, pocketing a big profit.

Then there was New Coke. "If I could have a New Coke every decade, it would be wonderful," Goizueta says. Sure, this was the greatest debacle in marketing history, but it alerted management that Coke's best asset is its brand--not the taste of the sugar water inside the can. After New Coke bombed in 1985, Coca-Cola overhauled its marketing; it has gained share against Pepsi every year since.

Now that he is ill, Goizueta's most important legacy may be his management team. The deep-thinking CEO has surrounded himself with strong-willed, hard-charging executives who get huge rewards, mainly in Coke stock, if they hit their economic profit targets. "Roberto has filled in behind him so well," investment banker Herb Allen, a Coke director since 1982, told FORTUNE for this story. "He established at least four people who can run the company after he decides not to run it anymore, and behind them are ten people who could fill their jobs. And how many people does Coke have who could become CFO? Between 15 and 25. I'm not exaggerating."

Still, all eyes are on Ivester--who, says Goizueta, possesses the qualities that are essential for a CEO to have. "Energy is No. 1," Goizueta says. "Intellectual courage is extremely important too--intellectual courage to go out and do something."

A self-made executive in every way, Ivester grew up as a factory foreman's son in Gainesville, Ga., 60 miles north of Atlanta. He graduated from the University of Georgia, then began his career as an accountant at Ernst & Whinney. He assumed he'd be there forever. Coke was Ivester's client, however, and in 1979 the company recruited him as assistant controller. Ivester met Goizueta, then an executive vice president, his first week.

It didn't matter that Ivester was shy and not very sophisticated. Goizueta says, "The way I judge our executives is not on personality or what they're like to be with socially, but whether they produce results." Ivester quickly showed himself to be ingenious at devising clever solutions to arcane financial problems--and, to Goizueta's pleasure, at maximizing returns on investment.

Goizueta tapped Ivester to be his chief financial officer six years later. Ivester made his mark immediately as the architect of the "49% solution," an innovative deal to get Coke's low-return bottling operations, along with their monstrous debt, off the company's books. With Goizueta's guidance, Ivester set up a separate bottling entity called Coca-Cola Enterprises (CCE). Coke spun off CCE to shareholders, keeping enough equity--yes, 49%--to heavily influence how the business is run. It was a classic play for Ivester (now CCE's chairman), who has said he looks at business "like a chessboard" on which he seeks to see "three, four, five moves ahead." CCE's stock has quadrupled in the past two years.

Goizueta and Ivester developed almost a father-son bond, not too unlike Goizueta's relationship with Woodruff. In the summer of 1989, Goizueta gave his CFO his first operating job, as president of Coke's European operations, and Ivester hit the ground running. The Berlin Wall fell that November. Within days Ivester was shipping carloads of Coke into East Berlin and cutting deals for bottling plants across Eastern Europe. Because of Ivester's gutsy opportunism, Coke seized control of the region, long a Pepsi stronghold.

Climbing Coke's ranks, Ivester worked methodically to fill his knowledge gaps. When he wanted to better understand antitrust issues, he set up evening sessions with Joe Gladden, Coke's general counsel. "If I don't know enough about a subject, I say, 'Let's have a session where you educate me.'" When he became president of Coke USA in 1990, Ivester felt he needed lessons on marketing. For a year he spent Saturday mornings with Sergio Zyman, now Coke's global marketing boss, over coffee and flip charts at Zyman's home. Ivester has since added a "chief learning officer" to Coke.

By will and ingenuity, Ivester became a better executive than anyone had expected him to be. Goizueta has worried from time to time that Ivester isn't tough enough ("He doesn't have enough impetus," he griped to FORTUNE just a year ago), but those who work for Ivester insist he has "impetus" to spare. "Doug is not a low-key guy," says Jack Stahl, president of Coke's North America Group. "He's as aggressive as anyone you're going to meet."

Visiting some 30 overseas markets a year, Ivester carries this message: "We want to capture all the growth." When he became president of Coke, he scrapped traditional-style goal setting and instead advocates "destination planning." Meaning: He tells managers to decide what kind of growth is possible in a particular market, then figure out how to knock down the barriers to getting there.

Whenever and however Ivester moves up, like Goizueta he will surely stick to one business, non-alcoholic beverages, because it's wonderfully profitable. "I'm never distracted by the periphery," Ivester says. Major management shifts are unlikely, mainly because Coke's senior team reports to Ivester already. Besides Ivester, the superstars Herb Allen presumably had in mind are Europe boss Neville Isdell, domestic chief Jack Stahl, and Doug Daft, who heads the Middle and Far East. Some people speculate that Stahl would become Ivester's No. 2. It's more likely that Ivester won't appoint a president for at least a while.

If Ivester becomes CEO soon, he'll have a lot to contend with. Coke's earnings outlook is worrying Wall Street. The problem isn't Coke's fundamental business--it's humming along fine. The strong dollar is hurting profits, though, and there's a slowdown in Coke's sales of its bottling businesses, which means fewer one-time gains. Coke shares, at $59, are down 19% from their June high. Most analysts, nevertheless, are still recommending the stock.

Should Goizueta's health hold up, it's not hard to speculate on what he might want to do next. Fancying himself a philosopher of corporate governance, he has long advocated the principle of companies' dividing responsibilities between a non-executive chairman (say, Goizueta) and a hands-on chief executive (say, Ivester). Oddly, Goizueta has never before seemed inclined to implement such an idea at Coke.

However the future plays out, Ivester's biggest challenge will not be running Coca-Cola. It will be coming up with a suitable act to follow the God-like role that Goizueta has been playing for years.