The move was a formality after a judge dismissed the case in London's High Court last week when the government cancelled the West Ham deal, saying it had become "bogged down" in legal challenges which threatened the date for the stadium's re-opening and its bid for the 2017 World Championships.
Tottenham had threatened to take various parties to court over legal costs, but all sides on Monday agreed to pay their own.
Third-tier club Leyton Orient, which had also challenged the stadium decision on the grounds that it could force them out of business, will pursue their case for legal costs against West Ham's bid partner Newham Council.
West Ham, who were relegated from the Premier league last season, could still end up renting the venue under a new plan to keep the stadium in public ownership although Orient chairman Barry Hearn stole a march on Tuesday when he formally applied to the Football League for his club to relocate to a slimmed-down, 25,000-seater Olympic Stadium.
"We have submitted an application for permission to move to the Football League, and that permission is something that West Ham don't have yet," Hearn said in a club statement.
"It was the Premier League who gave [West Ham] the green light to move in their original plan, but they are no longer members of the Premier League."
Tottenham, who have an alternative plan to build a new stadium adjacent to their current north London home, have yet to comment on whether they will bid to become tenants.
