"It's fantastic for everyone at West Ham United that at last all the club's hard work over the past three years has paid off," joint chairmen David Sullivan and David Gold said.
"Since we came to West Ham in 2010 we have had a vision to really take the club forward so West Ham United can compete on the pitch at the highest level.
"Today's decision offers us a real platform to do this and we are fully committed to making it a real success.
"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 honour we will take on with pride."