The former PayPal president will take the reins from Tim Morse, who will resume his role as chief financial officer, on January 9.
Thompson, who helped PayPal's revenue grow by more than $2 billion last year, will also join Yahoo's board of directors. His primary focus will be the firm's "core business", playing an active role in its investments and dispositions of assets.
"Yahoo is an industry icon and I am very excited about the prospect of working with one of the great teams in the online world to deliver Yahoo's next era of success," Thompson said.
"Yahoo! has a rich history and a solid foundation to build on, and its continued user engagement is one of the many reasons for my enthusiasm.
Roy Bostock, chairman of the Yahoo board added: "Scott brings to Yahoo! a proven record of building on a solid foundation of existing assets and resources to reignite innovation and drive growth, precisely the formula we need at Yahoo."
Last year, it was reported that Yahoo's quarterly profits have fallen by 26%. Co-founder Jerry Yang is rumoured to be preparing a buyout bid to take the company off the public markets.