The California-based company said the changes are a step towards a compromise with activist investor Daniel Loeb.
Loeb, CEO of Third Point and owner of 5.8 per cent of Yahoo's shares, has been agitating for a seat on Yahoo's Board of Directors in the hopes to implementing changes to the company's strategy.
Thompson, who was hired as CEO in January, will be replaced by Ross Levinsohn.
Thompson became the fourth Yahoo CEO to step down in the past five years.
Besides, five current board members, including director Roy Bostock and Patti Hart, will step down immediately and not end their terms.