Thompson is to be replaced on a temporary basis by Ross Levinsohn, head of global media, who will act as interim chief executive.
Questions over Thomspon’s qualifications emerged at the start of this month when activist shareholder Daniel Loeb of hedge fund Third Point accused Thompson of adding a bogus bachelor's computer science degree to his CV.
In addition to the CV controversy, a Wall Street Journal report said his decision was partly influenced by a recent diagnosis of thyroid cancer.
In a statement to investors, Yahoo declined to provide reasons for Thompson's departure. Yahoo last week launched an investigation into the CV issue and Thompson issued a memo to staff saying how "deeply I regret how this issue has affected the company".
Thompson's resignation comes just five months into his tenure, during which time he was responsible for enacting a company-wide restructure to cut 2,000 jobs.It was also under Thompson that Yahoo moved to sue Facebook over alleged patent infringement.
Previously president of PayPal, he took the reins from chief financial officer Timothy Morse, Yahoo's interim chief executive, in January after the board dismissed Carol Bartz in September.
Shortly after Thompson joined, Jerry Yang, co-founder of Yahoo, resigned from the board.
Board members Patti Hart, VJ Joshi, Arthur Kern and Gary Wilson, who all previously said they would not stand for re-election, announced they have stepped down from the board immediately.
The embattled digital company has also named Fred Amoroso as chairman, replacing Roy Bostock, who announced he was stepping down from his role in February amid a board shake-up.
As part of the company’s settlement with Third Point, Loeb as well as other Third Point nominees Harry Wilson and Michael Wolf, are joining the board effective from 16 May.
The company, which faces tough competition from Google and Facebook, has been struggling with its revenues in recent years, and under Thompson its strategy was to cut cost and refocus.
In its most recent financial results, Yahoo unveiled a slight increase in revenues for the first quarter of 2012 to $1.22bn (£767m), up 1% from the same period last year.