The East London club will become anchor tenants for the Stratford venue and should move there at the start of the 2016-17 season.
The Hammers had seen competition from Leyton Orient chairman Barry Hearn over the rights to the ground, but the Premier League club was named preferred bidders for the stadium by the London Legacy Development Corporation (LLDC) three months ago.
"I'm delighted that we have been confirmed today as the anchor concessionaire for the Olympic Stadium," West Ham vice chairman Karen Brady told the club's official website. "It was important to me that we struck a deal that would stand the test of time that represented the right deal for West Ham United and our loyal and patient supporters."
Initially, West Ham owners David Sullivan and David Gold were reluctant to pay anything toward the reconstruction of the stadium, but now are willing to put up 15 million pounds. Adapting the stadium could cost in total between 150-190 million pounds, with the rest of the money is being generated from sources such as the government and loans.
The roof will be extended and the seating capacity inside the stadium, which will slide over the running track, will be reduced from 80,000 to 54,000 under conversion plans, and it will be a UEFA Category 4 ground.
The Premier League club will be required to pay 2 million pounds a year in rent and has agreed to sell a portion of any future sale to the LLDC, with whom it is working to secure a deal to sell the naming rights of the stadium.
Sullivan and Gold praised the club's staff for their hard work, and said that the move will allow the club to compete at the highest level.
"Today's decision offers us a real platform to [compete at the highest level] and we are fully committed to making it a real success," the joint chairmen said in a statement. "We understand the responsibilities that come with calling the nation's iconic Olympic Stadium, which will be converted into a world-class football stadium, our new home. It is an honor we will take on with pride."