The proposed bridge, for which the competition organisers hope to gain commercial backing, is to span the River Thames from Temple Gardens, near Covent Garden, on the north bank to the London Weekend Television building near the South Bank Centre.
Designs, which are to be submitted by a shortlist of architects, will form the centrepiece of an exhibition at the Royal Academy of Arts in September. Sponsored by the Corporation of London, the exhibition will feature a river meandering through the main gallery at Burlington House, Piccadilly, spanned by models of historic and futuristic bridges.
Contemporary proposals for bridges across the Thames will also be represented, including Will Alsop's design of a home for the Institute of Contemporary Arts (ICA) at Blackfriars and the Peabody Trust's vision of a housing scheme between St Paul's Cathedral and Bankside.
Mr Gummer, who is also minister for London, said the concept of a habitable bridge in the capital harked back to the old London Bridge, which was stacked with houses and businesses and "on which people felt themselves to be a part of this great city". The minister said the purpose of a bridge should be to join, and not divide, London.
He added: "It is well-known that I wish to see the River Thames, one of our most unsung assets, playing a greater role in the life of London. This would be a bridge of confidence on which people would work, shop and live on the river itself."
The competition, sponsored by Thames Water, is a joint project between the Pompidou Centre in Paris and the Royal Academy. Jean Dethier, of the Pompidou Centre, whose research into habitable bridges inspired the project, said: "We are interested in the interdisciplinary approach of modern art and architecture and its ability to connect history with the present and the future. We are interested in the bridge as a non-segregational concept with a strong civic link."
Entries include the German architect Daniel Liebskind and two British firms, Future Systems and Branson Coates. The exhibition is being designed by Nigel Coates, professor of architectural design at the Royal College of Art. Mr Coates said he was planning to run a river through the gallery just below eye level, so that visitors could see into the designs.