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Olympic Park Legacy Company (OPLC) executives chose the club’s bid over a rival proposal from Tottenham Hotspur.
The decision must now be ratified by two government departments and the mayor of London, possibly next week.
The vote in favour of West Ham’s bid for the £537m venue was unanimous. It was judged to provide the best legacy.
Spurs’ plan was widely criticised because it would involve knocking down the stadium and building a new one.
The club intended to pay for an expansion of the athletics facility in Crystal Palace, rather than keeping a legacy for the sport in Stratford.
West Ham, currently bottom of the Premier League, will keep athletics in east London and leave the running track untouched.
Baroness Ford, head of the OPLC, said: “We have made a unanimous recommendation to back West Ham and the borough of Newham as the long term tenant.
“This represents the very best legacy for the stadium.
“It is cracking for the communities of east London and a really good outcome for sport.”
Baroness Ford claimed that, contrary to reports the recommendation was a foregone conclusion, it was a tough decision.
She said: “I pay tribute to both bids. They have each put the most enormous amount of effort into bringing the bids forward.
“We were thrilled to have two robust competitors.”
A Spurs spokesman said: “We provided a first class proposal to support the sustainability of the whole project.
“It was never an option, however, that we would retain the running track as we believe this unacceptable for our supporters.
The club added the deal was not yet concluded and it would “monitor the situation”.
West Ham are yet to comment.
A joint statement from Culture Secretary Jeremy Hunt and Communities Secretary Eric Pickles read: ”Today’s recommendation by the OPLC board marks an important milestone for the future of the Queen Elizabeth Olympic Park and the whole Olympic project.
“We will look through their recommendation in detail before coming to our own decision.
“We aim to make a formal announcement to Parliament shortly.”
It is considered highly unlikely that the government and Mayor of London Boris Johnson will not now rubber stamp the recommendation.
Reacting to the announcement, Mr Johnson wrote on Twitter: “Significant step forward today for the Olympic Park. Long-term future looking good.”
Ken Livingstone, Mr Johnson’s rival in the 2012 mayoral election, said: “This is the right decision for Londoners, the right decision for sports fans and athletes and the right decision for those who are working to deliver a long-term Olympic legacy for the capital.
“Today’s decision will ensure we fulfil promises that the capital will retain a world class athletics stadium at the Olympic Park which will inspire future generations.”
UK Athletics boss Ed Warner also welcomed the decision.
He said: “The pledges have been met and there will be a long-term athletics legacy in the Olympic Park.
£95m project “We now have a fantastic opportunity to ensure it continues to inspire for generations to come.”
It is expected to cost about £95m to convert the venue from an 80,000 seat stadium to a 60,000-seat venue for football, athletics and cricket.
The Olympic Delivery Authority is to give £35m of that to West Ham, while most of the remaining funds have been provided by a £40m loan arranged by Newham Council.
But Lord Sugar, former chairman of Spurs, has previously said the West Ham plan is “totally flawed” and predicted the stadium would become “a white elephant”.
“It will be a disaster for the taxpayer and we’ll end up having a mothballed Olympic village,” he said ahead of the announcement.
The entertainment company AEG, who were partners in the Spurs bid, predict the stadium will go bust within a decade if it retains an athletics track.
But there was jubilation in north London among Spurs supporters who had campaigned against the club leaving its historic area.
Tim Framp, of Tottenham supporters’ group We Are N17, said: “Our initial reaction to the news is one of relief.
“We don’t want to be in any part of London apart from the bit we belong in.”
Tottenham MP David Lammy told BBC Sport: “Spurs leaving would be devastating for the local community.
“It’s hard to put into words how important Spurs is.”
Haringey Council also praised the decision. It stressed that Spurs have planning permission for a new stadium at the White Hart Lane site and said building could “start almost immediately”.
