Amazon will have no role in the acquisition and Bezos will become the sole proprietor of the Post when the sale is completed, probably within 60 days.
The transaction was kept secret until Monday.
"The Post could have survived under the company's ownership and been profitable for the foreseeable future," Washington Post Company chairman Donald Graham said. "But we wanted to do more than survive. I'm not saying this guarantees success but it gives us a much greater chance of success."
Katharine Weymouth, the niece of Donald Graham and the fourth generation of her family to be involved with the paper, will remain as publisher and executive director of the firm, although Bezos will be the owner.
"We have found an owner who will continue the tradition that the Graham family started," Weymouth said in a memo to the newspaper's staff.
Bezos said that the historic publication, founded in 1877, is an important institution and expressed optimism about its future.
"There is no map, and charting a path ahead will not be easy. We will need to invent, which means we will need to experiment," he said, while emphasizing he will have no part in managing the paper on a day-to-day basis.