Plans for the museum, to be situated next to the landmark Orbit Tower in the Olympic Park in a formerly rundown part of east London, are for it to open in 2014 with visitors likely to be charged "a modest entry fee".
"As the only city to have earned the honour of hosting the Olympic Games three times, London occupies a truly unique place in Olympic history," said BOA chairman Colin Moynihan in a statement.
"I believe the British Olympic museum is the perfect way to ensure the spirit, excitement and unforgettable memories of the London 2012 Games live on to inspire future generations to follow their own dreams."
London hosted the 1908 and 1948 Games but there are few relics of those earlier Olympics which used the White City and Wembley stadiums in the west of the city.
The International Olympic Committee has its own museum in Lausanne, Switzerland, while 1992 Games host city Barcelona also has one.
IOC president Jacques Rogge welcomed the initiative as something that would "become part of the lasting legacy that London 2012 will leave the UK for generations to come."
BOA BOA.L chief executive Andy Hunt said the museum, whose design and content were under discussion, would cost 10 million pounds to develop and operate for the first three years before breaking even and becoming cash generative.
"Our plans are to build a really leading attraction within the Olympic Park," he told reporters.
Hunt said the BOA would work with their own sponsors and try to raise funds from the IOC's top Olympic partners to pay for the museum as well as seeking a possible heritage lottery contribution.
"The 10 million pounds we are actually going to go out and fundraise," he said. "We will commence that before the Games. There is interest from the IOC top partners.
"This will sit within a charitable entity, the British Olympic Foundation, and we will use a professional operator for this kind of attraction," he added.
"It is not our intent to become an operator...we are not in any way putting financial risk onto the BOA."
(Reporting by Alan Baldwin, editing by Justin Palmer)
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