The Premier League club had sought a judicial review after the Olympic Park Legacy Company (OPLC) awarded West Ham preferred bidder status for the 486 million pound stadium earlier this year.
Spurs and West Ham, now in English football's second tier, both want to move into the venue in Stratford, east London, after next year's Games.
It is not clear whether Spurs will pursue their legal case or whether they will use Wednesday's decision to strengthen their hand in long-running talks with the government and Mayor of London Boris Johnson over a possible alternative new stadium next to their current site at White Hart Lane.
The decision puts in doubt London's planned bid to host the 2017 athletics World Championships because Tottenham would take out the running track as part of its development of the stadium.
Sports minister Hugh Robertson has said he wanted the issue settled by September to allow the bid to proceed unhindered.
Tottenham were not immediately available for comment. Their fans would prefer to stay in north London rather than move east, and fans celebrated when Spurs lost their bid for the Olympic stadium in February.
Building a new multi-million pound stadium near their existing site, as part of the Northumberland Park project which would also include shops and housing, would provide an economic boost to one of the most economically deprived areas of London.
High youth unemployment was one of the reasons given for this month's riots in England which began in ethnically diverse Tottenham after police shot dead a black suspect.
The riots have added new urgency to the talks, and the mayor's office had said only hours before the High Court decision that they were "hopeful" a deal could be reached.
FULL HEARING TO COME
Judge Andrew Collins, on hearing the appeal, gave Spurs permission to mount a legal challenge, the Press Association reported. The decision overturns an earlier failed attempt by Spurs in the High Court.
"We are waiting to hear from Tottenham Hotspur on their plans to rebuild on their current site before any agreement on financial support from the Mayor can be confirmed," a spokesman for the mayor said in a statement.
A Department for Culture, Media and Sport spokesman said: "We have noted the judge's decision today. The matter is in the hands of our lawyers."
West Ham plan to retain the athletics track and reduce the capacity to 60,000 from 80,000 before moving in for the 2014/15 season.
The judge's task at this stage was only to decide whether Tottenham had an "arguable" case.
A further hearing with full arguments from all sides will now have to be held, starting October 18, PA said.
"We are disappointed that permission for a judicial review has been granted on some limited points but we are confident in our case," Baroness Ford, OPLC chairman said in a statement.
Lawyers representing Spurs had argued West Ham had been given an unfair economic advanta
