The company said it agreed to buy the shares from Third Point LLC, led by activist investor Daniel Loeb, at Friday's closing price of $29.11 per share.
After the transaction Third Point will hold some 20 million shares, or less than two percent of Yahoo!'s outstanding common stock.
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The company also said that Loeb and two of his associates, Harry Wilson, and Michael Wolf, have submitted their resignations from Yahoo!'s board, effective July 31.
The board will then have seven members including Max Levchin, who was appointed as a director upon mutual agreement between Third Point and the board.
'Daniel Loeb had the vision to see Yahoo! for its immense potential, the potential to return to greatness as a company and the potential to deliver significant shareholder value,' said Mayer.
'On behalf of the board and our entire team, I'd like to take this opportunity to personally thank Dan, Michael, and Harry for the tremendous opportunities they created here at Yahoo!'
Third Point boosted its stake last year and sought changes in management after Scott Thompson was named chief executive.
Thompson resigned after acknowledging an error in his resume, which wrongly indicated that he had a degree in computer science.
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