That includes such things as Yahoo's online search, Yahoo Mail and instant messaging, and - perhaps most importantly - its ad business.
Yahoo first announced it was on the chopping block earlier this year several firms had been circling with interest in the dot-com giant which at one point was worth more than $100bn.
Verizon last year snapped another golden oldie of the dot-com era, getting AOL for a bargain $4.4bn (it had been worth more than $200bn at its peak and $350bn during its combined - but ultimately unsuccessful - time with Time Warner).
“Just over a year ago we acquired AOL to enhance our strategy of providing a cross-screen connection for consumers, creators and advertisers," said Verizon chairman and chief executive Lowell McAdam.
"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."
Verizon will integrate Yahoo with AOL, under Marni Walden, Verizon's executive vice-president of product innovation and new business - the combined digital media businesses have bigger combined audience than Google.
The deal is expected to close in the first quarter of next year.
Yahoo will keep hold of its cash, its shares in Alibaba Group and Yahoo Japan as well as convertible notes and some minority investments, and it will be renamed, becoming a publicly traded investment company. It plans to return its cash to shareholders.
The stakes in Alibaba nad Yahoo Japan are the more lucrative parts of the business compared to the online division.
“Yahoo is a company that has changed the world, and will continue to do so through this combination with Verizon and AOL," said Yahoo boss Marissa Mayer.
"The sale of our operating business, which effectively separates our Asian asset equity stakes, is an important step in our plan to unlock shareholder value for Yahoo. 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.”
There had been speculation that Mayer would depart once the deal was announced, however, in a note to employees, she said she would remain in place.
Shares in Yahoo fell more than two per cent as markets opened in the US while Verizon stock was largely flat, down 0.5 per cent at pixel time.