West Ham's Joint-Chairmen David Sullivan and David Gold said:
"'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. 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.''
In a statement posted on West Ham's website, the club's Vice-Chairman Karren Brady said:
"I'm delighted that we have been confirmed today as the anchor concessionaire for the Olympic Stadium. I commend my two Chairmen for their passion and commitment.
"I am delighted this has been rewarded now that their ambition to see the Club they love enjoy a bright future at the Olympic Stadium has been realised.
"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.
"The consultation we have promised them will now begin and we can't wait to work with them to create a stunning new home that befits the pride, passion and tradition that the world associates with West Ham United."
Londoners have been given a glimpse of the future of the Olympic Stadium.
Computer generated images of the venue have been released, showing it in its new role as home to West Ham football club.
The pictures reveal what match-days at the stadium might look like.
Olympic legacy bosses have revealed the new logo for the Olympic Park, which is being renamed the Queen Elizabeth Olympic Park.
Olympic legacy bosses hope naming rights will offset some of the cost of converting the 2012 stadium.
Estimates for replacing the roof and installing retractable seats over the running track range from £150m-£200m.
If £200m, the final bill for the stadium will be almost £630m - still cheaper than Wembley!
City Hall regards West Ham's £15m contribution as one of the triumphs of the "long and tortuous" negotiations.
WHUFC's initial offer towards conversion costs was zero.
Details of the future of the Olympic stadium will be announced this morning.
It's believed that West Ham football club have finally come to an agreement that will allow them to take over the stadium.
They're expected to take the stadium on a 99 year lease.
The negotiations between the London Legacy Development Corporation and West Ham have been long and tortuous since the club was named preferred bidders in December, but they have now finally been signed off by the corporation's legal advisers.
The agreement should also open the way for the stadium to be used as a venue for the 2015 Rugby World Cup.
But the deal does come at a cost to taxpayers- converting the stadium, including reducing it's capacity, will cost as much as £200m.
A large proportion of that will come from the government.