The Hammers were named preferred bidders in December but negotiations with the London Legacy Development Corporation (LLDC) have been long and tortuous.
However, the LLDC announced this morning that a deal has now been signed off that sees the Barclays Premier League club become anchor tenants under a 99-year lease.
Plans for the revamped stadium were unveiled this morning, with the reported £150million facelift due to be completed in time for the 2016-17 season.
The Olympic Stadium will be transformed into a 54,000-seater venue, with the Hammers now set to embark on a detailed, independent supporter consultation process.
"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 [Friday'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."
London mayor Boris Johnson was at the announcement made near the stadium this morning, along with mayor of Newham Sir Robin Wales and LLDC chief executive Dennis Hone.
"This is a truly momentous milestone for London's spectacular Olympic Stadium ensuring its credible and sustainable future," Johnson, who is also chair of the LLDC, said.
"Through this deal with West Ham United FC, we are defying the gloomsters who predicted this landmark would become a dusty relic.
"With a series of world class entertainment and sporting fixtures already in the bag for Queen Elizabeth Olympic Park, this iconic site is set to be the glittering centrepiece of ambitious regeneration plans for east London, which will capitalise on the Olympic investment into this area for the long term benefit of this city."
As expected, it was confirmed that the LLDC will receive a windfall payment should West Ham's owners sell on the back of the move within 10 years.
The stadium itself will have retractable seats all around the pitch, which will allow the 2017 World Athletics Championships to take place as planned. In addition, the deal opens the way for the stadium to be used as a venue for the 2015 Rugby World Cup.
The plans for the future of West Ham's current Upton Park home and the surrounding area remain confidential for the time being.
Leyton Orient owner Barry Hearn has been against West Ham taking over as the sole football club at the stadium and has challenged the decision throughout the process.
The 64-year-old Matchroom Sport chairman told talkSPORT he did not understand the timing of the announcement.
"I don't know why they are announcing anything because we have applied to the High Court for a judicial review of the bidding process, so anything they announce about West Ham has to be subject to the High Court's decision," he said.
"Why they are trying to steamroll this announcement through today [Friday], prior to the court's decision, to me is a sign of panic. I don't know why they are doing it."
Hearn's main bone of contention is his feeling that a move for West Ham closer to the home of npower League One club Orient will ruin his club.
"We don't think we have been given a fair crack of the whip," he said.
"We have had no opportunity to discuss ground-sharing with West Ham, which we think is the only logical way out. What harm do we do? We get a chance to survive."