The Quintain application, which was submitted in October, was agreed by Brent council last week. It is now due to be reviewed by the Greater London Authority and the Government Office for London.
The scheme is expected to create more than 1000 construction jobs and cost £1.3bn.
It is due to be completed in 2006 at the same time that Wembley National Stadium opens.
Quintain is expected to sign a series of joint-venture deals to help it finance, build and run various aspects of the scheme.