Bezos is buying the Post as an individual, not on behalf of Amazon.
"Jeff Bezos' proven technology and business genius, his long-term approach and his personal decency make him a uniquely good new owner for the Post," said Donald Graham, CEO of the Washington Post.
Washington Post shares shot up more than 5 percent after-hours, topping $600 a share. What are Washington Post shares doing now? (Click here for the latest quote)
Amazon shares were flat. (Click here for the latest quote.)
The transaction covers the Washington Post and other publishing businesses, including the Express newspaper, The Gazette Newspapers, Southern Maryland Newspapers, Fairfax County Times, El Tiempo Latino and Greater Washington Publishing.
AllThingsD reported that Bezos wasn't the only bidder interested in the newspaper, but he was the "best and highest bidder," according to sources. Media bankers Allen & Co. ran the auction.
Bezos said, "I understand the critical role the Post plays in Washington ... and our nation, and the Post's values will not change. Our duty to readers will continue to be the heart of the Post, and I am very optimistic about the future."
John Morton, newspaper industry analyst and president of Morton Research, said he was stunned by the deal and the Graham family's decision to sell a newspaper they have been closely identified with since the 1930s.
"To me, it was inconceivable that [the] family would allow to this to happen, but from a financial point of view you can understand some of the reasons for it," he said. Morton said the newspapers have been a problem area for a while and clearly affected the stock price.
Some traders weren't sold on Bezos's ability to turn a profit at the newspaper unit.
Bezos "certainly has a history of running companies at low levels of profitability," Brad Safalow, founder and CEO of PAA Research, said on CNBC's "Fast Money." "I don't really see a scenario in which the Washington Post can be run as a profitable entity, but maybe that's not really his objective here."
(Read more: What Post sale means for company, Bezos: Pro)
This is the second newspaper deal in the past few days. On Saturday, the New York Times Co. agreed to sell The Boston Globe and its other New England media properties to John Henry, principal owner of the Boston Red Sox, for $70 million.
(Read more: New York Times Co. Sells Boston Globe)
The Washington Post deal does not include Slate magazine, TheRoot.com or Foreign Policy magazine.
The Washington Post Co., which also owns Kaplan, the education testing business, will change its name within 60 days of completing the transaction, according to an SEC filing.
The stock price could move higher now that the company is shedding its newspapers, according to Morton.
"The assets are attractive, and the company would attract a higher stock price because it would be unencumbered by the newspaper weighing it down," he said.
Buffett's Berkshire a big shareholder
Warren Buffett's Berkshire Hathaway has a big stake in the Washington Post Co. As of March 31, it owned more than 1.7 million shares—almost one-quarter of the shares outstanding—worth almost $1 billion.
The Washington Post Co. has a market cap of $4.2 billion.
Buffett has a long-standing connection to the Post, including a friendship with late publisher Katharine Graham that started in the 1970s. He began serving on the company's board in 1974, just after Berkshire bought its stake, and reluctantly retired from it in 2011, after what he called a "great 37 years."
At the time he said, "I've loved The Washington Post since I delivered almost 500,000 copies of it as a youth in Washington. That love for the product, the company and the management continues unabated today."
Buffett told The Wall Street Journal that he would "never sell a share" of the Post because it has "all kinds of meaning to me."
A Berkshire spokesman said Buffett did not immediately have a comment about the Bezos sale.
Even though he once said the newspaper industry has a "terrible" future, Berkshire has been buying community-oriented newspapers in small to midsize cities, including the Omaha World-Herald in his home town. Buffett believes such properties' monopoly on local news and information allows them to compete effectively with digital news sources.
At Berkshire's annual shareholders meeting in May, Buffett told CNBC that he doesn't expect to "move the needle" with the newspaper buys but thinks they will generate an annual return of 10 percent—so "we're not doing anything dumb."
—By CNBC's Justin Menza and Alex Crippen