The club, who move to their new ground in 2016, plan to develop the London venue to a 54,000 all-seater capacity and Uefa category four eligibility - the highest standard for stadiums in European football.
West Ham will also create new hospitality suites and construct a new ticket office and club store of the Olympic site.
"This is another key milestone on our journey to Stratford and my board and I are delighted with the decision," vice-chairman Karren Brady told the club's official website.
"We always knew that the innovative plans for the Olympic Stadium could create a globally-recognised football stadium and we were confident that planning permission would be granted to allow the conversion work to begin.
All that's left now is for the Mayor of London, Boris Johnson, to approve the plans before the transformation can begin later this year. For me and my team the hard work is only just beginning.
"This is an incredible opportunity to create a world-class stadium for West Ham supporters that will exceed their expectations and the chance to really deliver a lasting legacy for London."