The museum, set up in 1996 to house 40,000 military artefacts, faced going into receivership two years ago after attracting less than half its target number of visitors.
The Department of Culture, Media and Sport (DCMS) bailed it out with a deal which the National Audit Office (NAO) says was more expensive than other possible options.
The Royal Armouries was one of the first projects to be set up under the previous Conservative government's private finance initiative scheme, which uses private sector money to fund large public building projects.
A private sector consortium, Royal Armouries International (RAI), was set up to invest £14m in the site and manage the museum, which cost £42m in total.
But with visitor numbers peaking at 344,000, instead of a projected 800,000 a year, the museum was faced with closure after the company running it amassed a £20m deficit.
It was saved by a restructuring agreement that saw RAI handing over the running of the museum to its public partner, Royal Armouries, which owns the artefacts.
Taxpayers' bill
The DCMS agreed to continue funding the museum with an extra £1m a year on top of its existing £4m annual grant.
The NAO said: "The end result is that the government, and not the contractor, will pay to keep this museum open."
Taxpayers will now foot a bill which could total £25m over 25 years, it warned.
Sir John Bourn, head of the NAO, said ministers chose an option which was significantly more expensive than other possible solutions.
'Unrealistic projections'
David Davis MP, chairman of the influential Commons public accounts committee, said: "I am concerned that when confronted with the financial crisis, the department did not strike a more commercial deal.
"Like the Millennium Dome, the financial feasibility of this high-risk project was based on projections of visitor numbers that proved to be wholly unrealistic.
"And again in this case, there were no contingency plans in place should visitor targets not be met."
Mr Davis, Conservative MP for Haltemprice and Howden, said the case showed the private finance initiative was not a "magic wand" that removed all risk from the public sector.