The role has been vacant since the company fired Carol Bartz in September. Thompson will relieve Yahoo's interim CEO Tim Morse, who will return to his position as chief financial officer.
Thompson has served as president of eBay's payment division since 2008. Yahoo's announcement points out that under his leadership PayPal more than doubled both its active userbase and its revenues.
He will begin his tenure as Yahoo CEO during an uncertain time at the company. Several private equity firms have reportedly expressed interest buying a 20% minority stake in Yahoo, and Microsoft signed a confidentiality agreement with Yahoo in November to get access to the company's financial information, which could be the first sign of a potential buyout. Microsoft famously attempted to purchase Yahoo in 2008 for a reported price of more than $44 billion.
Meanwhile, the company is reportedly selling its holdings in China and Japan.