"Much has been made of the promise to keep the athletics track within the Olympic Stadium and, therefore, we should all expect to see the retention of this track firmly embedded and legally guaranteed by those entrusted with this legacy commitment, today and in the future," the statement read.
"The OPLC's decision has still to be approved by two Government departments and the Mayor's Office. We shall continue to monitor the bid process over the coming weeks up until its final determination, whilst reviewing our position and holding discussions with our advisors."
Assuming West Ham's move is rubber-stamped, Tottenham are expected to push ahead with their plans to build a new £400m stadium on the site on their current home at White Hart Lane.
Stadium pick 'proud day for nation' - Gold
Spurs boss Harry Redknapp said West Ham would lose a lot of the atmosphere of Upton Park if they move to a ground with a running track.
"Good luck to them if that's what the fans want [but] I wouldn't want to watch football matches with a track around [the pitch]," said Redknapp, who West Ham manager between 1994 and 2001. "There is no atmosphere."
News that their Olympic bid had fallen through was greeted with delight by Spurs fans' group We are N17 which had staged protests against the proposed move to a site five miles away from White Hart Lane.
"It is probably the only time in my life I have or will celebrate a victory for West Ham," said We are N17 spokesman Tim Framp.
"I actually feel a bit sorry for some of the West Ham fans that are going to be sat in that stadium because I don't actually think either bid was particularly great.
"I don't understand why both clubs were so desperate for that stadium. I don't feel like any club has particularly won."
West Ham fans have generally been more ambivalent about the move, with the club recently highlighting a Premier League poll showing that more than 50% of Hammers supporters had positive feelings towards the proposed switch.
But Sam Haseltine, author of the
West Ham Process
blog, said the prospect of sharing a multi-purpose ground with athletics, cricket, concerts and other community events was a turn-off for many fans.
He told BBC Sport the news had left him with a "bittersweet" feeling.
"It would have been worse for us had Spurs got it," he said. "So I'm pleased about that, but I'm very dubious about the plans.
An artist's impression of Tottenham's proposed 60,000-capacity stadium
"West Ham fans want a legacy of football. I, and many others, couldn't care less about protecting athletics, making sure we provide for other sports.
"We have compromised too much of what we actually are. We are a football club, not a multi-sports arena. We [will] moved to a stadium which suits everybody except for us. That frustrates so many fans."
West Ham's proposed move to the Olympic stadium could have a major impact on League One club Leyton Orient, whose Brisbane Road home is only two miles from the Stratford venue.
Orient chairman Barry Hearn has said either club taking over the Olympic stadium would contravene Premier League and Football League rules over clubs moving into the "immediate vicinity" of other clubs.
But Premier League spokesman Dan Johnson told BBC Sport the league had already approved the proposals.
"In examining all our criteria set out in our rules there was no reason why either club shouldn't move to the Olympic stadium," he said.
Johnson's assertion will not stop Orient fans fighting against the decision.
Stratford decision 'pivotal' to Palace stadium plans
"We've got a meeting of the fans's trust on Saturday where we will cement our plans," Doug Harper, chair of the Leyton Orient Fans' Trust," told BBC Sport.
"I'm sure we will be lobbying the Premier League. It is just the start now. We will be working with the club and others.
"West Ham are not going to fill a 60,000-seat stadium and have said they are going to offer cash incentives. That would stamp on our turf in this day and age when money is tight.
"It is OK in terms of the current Leyton Orient fans but what about the younger ones? Which will they choose if we have Swindon on a Wednesday and West Ham are playing Manchester United?"
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