The Olympic Park Legacy Company picked West Ham as its preferred tenant for the 537 million-pound ($867 million) stadium, which will stage the opening and closing ceremonies and track and field competition in 2012.
OPLC chairwoman Baroness Margaret Ford said the decision by the 14-member board was unanimous.
The decision, which followed months of fierce debate and rancor between the two clubs, still requires ratification by two government departments and the London Mayor's office.
"It's great for Londoners, very good news for the UK taxpayer ... and a very good outcome for sport," Ford said at a news conference.
West Ham plans to downsize the stadium from 80,000 to 60,000 seats and use it as a multipurpose venue that includes the Olympic running track. The Hammers hope to move into the stadium from their current Upton Park home in nearby east London in August 2014.
"Today is a momentous day," West Ham vice chairman Karren Brady said. "We are proud to have been passed the Olympic torch and fully embrace the responsibility we have for keeping the flame alive."
Tottenham, bidding with American sports and entertainment giant AEG, had proposed taking down most of the stadium and putting up a 60,000-seat football-only stadium on the same site without a track. Tottenham's plan had been widely criticized by Olympic officials and athletes.
Tottenham indicated earlier this week that it could mount a legal challenge to a decision in favor of West Ham's bid.
London Olympic leaders promised to keep an athletics legacy at the stadium when they made their successful bid to the International Olympic Committee in 2005.
Brady claimed this week that Tottenham's plan to tear down the stadium would be a "corporate crime." Sebastian Coe, the former running great who heads the London Olympic organizing committee, said recently that Britain had a "moral responsibility" to keep the stadium track. He said Britain would "trash" its international reputation if it went back on its promise.
In order to provide a track and field legacy, Tottenham had offered to redevelop the crumbling Crystal Palace athletics stadium in south London.
Friday's decision was welcomed by the British Olympic Association as a "victory for athletes, for sport and generations of young people." "This is also a victory for the reputation of British sport globally," the BOA said.
Tottenham and AEG say West Ham's attempt to combine football and athletics isn't economically viable in the long term and the stadium will become a white elephant - especially as West Ham is currently in last place in the Premier League and facing demotion from the top flight.
Once the deal with West Ham is ratified, the club must enter into contract negotiations with the OPLC.
If final agreement isn't reached by the start of April, the process could start over again.
"We will look through their recommendation in detail before coming to our own decision," Culture Secretary Jeremy Hunt and Communities Secretary Eric Pickles said in a statement. "We aim to make a formal announcement to Parliament shortly." West Ham is based closer to the Olympic Park in Stratford, east London, than Tottenham, which plays at White Hart Lane 9 kilometers (51/2 miles) away in a northern suburb.
West Ham is bidding jointly with Newham Council, the local authority, which will provide a loan of 40 million pounds ($64 million) to the club.
West Ham also hopes to stage concerts at the stadium in conjunction with promoter Live Nation Entertainment as well as Twenty20 cricket and American football. The stadium refurbishment is expected to cost 100 million pounds ($160 million).