The free exhibition about the history of the competition, Olympic Journey: the Story of the Games, will run throughout the games.
The exhibition will show objects on loan from the Olympic Museum in Switzerland, which is shut for refurbishment. It will be the biggest partnership between the museum and a host country so far.
Several rooms in the Royal Opera House will be devote to the exhibition, which will include a hall of champions and a display of every Olympic torch since 1936.
But questions have been asked about why the exhibition was not offered to a London museum or gallery.
The London Organising Committee of the Olympic Games (Locog) said the Royal Opera House had been chosen because of its central location in Covent Garden and because it is closed during the summer season.
According to a Locog spokeswoman, sponsor BP started talks with the Olympic Museum. “They wanted to have the exhibition somewhere that would reach a wide audience and attract people who wouldn’t normally come.”
The exhibition is part of the London 2012 Festival, the finale of the Cultural Olympiad programme that has been staging cultural events across the UK in the build-up to the games.
Most of London’s national museums are staging exhibitions during the festival. The British Museum and National Gallery are planning blockbuster exhibitions, while the National Portrait is hosting the Road to 2012 project.