The announcement was expected after media reports on Friday said the two companies were in exclusive talks over a possible deal.
Yahoo announced in February that it was looking at "strategic alternatives" for its core internet business, subject to shareholder and regulatory approval. It has struggled of late after reporting a $4.36bn yearly loss for 2015.
Verizon, which bought AOL in May last year, will now integrate Yahoo with AOL under Marni Walden, executive vice president and president of the product innovation and new business organisation at Verizon.
Marissa Mayer, the chief executive of Yahoo, said the sale of the company's operating business is an important step in its plan to unlock shareholder value.
She said: "This transaction also sets up a great opportunity for Yahoo to build further distribution and accelerate our work in mobile, video, native advertising and social."
Combined, AOL and Yahoo will have more than 25 brands in its portfolio for continued investment and growth. Yahoo’s key assets include content brands across finance, news and sports, as well as one of the most popular email services in the world with about 225 million monthly active users.
Lowell McAdam,Verizon's chairman and chief executive, said: "Just over a year ago we acquired AOL to enhance our strategy of providing a cross-screen connection for consumers, creators and advertisers.
"The acquisition of Yahoo will put Verizon in a highly competitive position as a top global mobile media company, and help accelerate our revenue stream in digital advertising."