The London Legacy Development Corporation - which manages the publicly-owned stadium - has been told to publish details of the move.
London mayor Boris Johnson, who oversees the LLDC, says he is "perfectly happy" with the decision.
West Ham say it will prevent them "securing the best deal for taxpayers".
The club were awarded tenancy of the London 2012 stadium in 2013, and £272m has been spent to convert the site for use as a Premier League ground.
West Ham have contributed £15m towards those costs, and will pay between £2m and £2.5m a year in rent. Last month a BBC documentary revealed that the club was having many of the running costs of the stadium paid for it by the taxpayer under the terms of the tenancy agreement.
A coalition of 14 supporters' trusts from around the country submitted a Freedom of Information request to obtain that tenancy agreement and believe that the deal gives West Ham a competitive advantage.
Manchester City pay council rent of about £4m a year for the Etihad Stadium, the construction of which was also initially funded by taxpayers, for the 2002 Commonwealth Games.
It has been reported that Chelsea and Tottenham may have to pay between £11m and £15m a year to play at Wembley if they use the national stadium temporarily while they redevelop their grounds.
West Ham have joined the LLDC in insisting that the rental deal should remain private for reasons of commercial confidentiality.
Speaking at mayor's question time on Wednesday, Johnson said he is happy to have the details made public but believes that the deal remains the best available for the taxpayer.
"We did not want to put anything out that would impact on our ability to negotiate future contracts," Johnson said.
"But it should be a matter of public record and we should be very proud that we have got a Premier League football team in that stadium.
"The stadium has been a fantastic success. It is doing brilliantly and it is basically unlike any other Olympic Stadium around the world as it has a long-term viable future with Premier League football at the heart of the deal.
"There are Olympic stadiums around the world that are totally mothballed and don't have any real activation in them. Go to Athens, go to Beijing.
"We've got nothing to hide, we've got a very good rental agreement with West Ham and it's fantastic that we will not be spending any more public money on this."
Under the terms of the deal West Ham have a 99-year deal as anchor tenants, and the LLDC says future profits will see a return to the taxpayer.
A West Ham spokesman said: "West Ham United shares the mayor's view that our presence at the former Olympic Stadium guarantees it a viable and sustainable future.
"Our agreement will not only return hundreds of millions of pounds to the taxpayer, but will ensure that London's Olympic Stadium will not join the long list of other former Olympic stadiums that are rotting away through lack of use.
"The LLDC has stated its disappointment at the Information Commissioner's Office ruling as it believes it will damage its ability to secure the best deal for the taxpayer in future and we share those sentiments.
"The club are now working with the LLDC to decide the appropriate next step."
West Ham say they are "disappointed" with a ruling that the terms of their rental of the Olympic Stadium from next season should be made public.