By Adam Lashinsky

(FORTUNE Magazine) – EVEN FOR A BUSINESS BUILT AROUND oddball purchases, the decision by eBay to acquire the free voice-over-Internet company Skype--for as much as $4.1 billion--in mid-September appears at first to be pretty goofy. Consider the strained business rationale. While most deals come packaged with one easy-to-digest line about synergies, eBay needed a 78-page PowerPoint presentation to explain its purchase, offering a hodgepodge of suggestions on how it could build Skype into its business. At the same time, CEO Meg Whitman made sure to point out repeatedly Skype's value as an incredibly fast-growing stand-alone phone business. (In early 2004, Skype had 2.4 million registered callers worldwide; that number is now over 54 million.) "I would characterize it as an effort for us to continue to keep expanding the eBay marketplace," tried out Whitman over breakfast a few days later.

Making the two businesses work well together is sure to be a challenge, even for a management star like Whitman. eBay has long since joined the establishment. Skype rejoices in taking on the established. Founders Niklas Zennström and Janus Friis made their name creating Kazaa, at one time the single best way to steal songs on the Net. (They still don't enter the U.S. for fear of being subpoenaed.) The pair built Skype using Estonian computer geeks and chose tax-haven Luxembourg as their base.

Whitman was introduced to Zennström by a mutual friend in Beijing this past May while she was attending the FORTUNE Global Forum and he was trudging through Asia hammering out partnerships. Zennström isn't worried about a culture clash. "The plan is business as usual," he insists. "We're getting a big brother now, and we can use a lot of their toys."

Cultural fit or not, eBay felt it had little choice but to act: This summer its biggest challengers--Google, Microsoft, and Yahoo, all of which offer avenues for buyers and sellers to find one another--acquired or launched technology allowing their users to call each other online. eBay was falling behind and decided to buy the best-known brand in the business. "Keeping up with the Joneses is a good way to explain it," says Yankee Group analyst Patrick Mahoney. The market is unimpressed: eBay's stock is down 7% since merger rumors broke.

But if the reaction on Wall Street has been muted, observers in Sweden and Estonia have virtually declared a national holiday. Under the headline ZENNSTROM HAS MADE HISTORY, Stockholm business magazine Affärsvärlden wrote that the Swede "deserves his own chapter in Swedish business history books." If eBay can figure out the best way to monetize its own fast-growing new toy, he may get his own book.

-- Adam Lashinsky and Daniel Roth