The £700m project backed by the FA is a scaled-down version of the original design by Foster and Partners, which does not include the hotel, office development and visitor centre that was originally intended.
Contractor Multiplex agreed to shoulder the risk for the construction costs, estimated at £400m, after a government decision not to put any more public money into the project.
It emerged that Multiplex is being investigated as part of an inquiry into corruption in the Australian construction industry.
The move will be viewed as a triumph for London mayor Ken Livingstone, who has campaigned to keep the national stadium at Wembley. But the move has undermined the hopes of bids from Coventry and Birmingham.
The existing Wembley stadium is due for demolition in summer 2002, with construction of the new stadium to be complete by 2005.
Lord Foster said: "The reborn stadium will become a proud symbol for the nation and for visitors around the world."