The green light from Westminster City Council (WCC) means the Grade II-listed baths - designed by K M B Cross and A W S Cross and opened in 1932 - will be taken off English Heritage's 'Buildings at Risk' register. They were put on the register after their closure in 1997 for safety reasons.
The project will include the restoration of the baths - famous for their stunning barrel-vaulted roof - as well as a wider development of the site, with a new purpose-built leisure centre opening in the first half of 2009.
The new leisure centre will see the original marble-lined pool restored, along with the building of a new gym and health suite, including dance and exercise studios.
As part of the development, by the Marshall Street Regeneration consortium (formed from Resolution Property and Vinyl Factory), 52 new homes will also be built, 15 of which will be affordable.
Finch Forman project architect Ian Eggleton said: 'Finch Forman is dealing with everything in or on the existing building, and Munkenbeck & Marshall is on the same site but doing new build from the ground up.'
Under the scheme the building's car park will also be upgraded and reduced in size and a new street-cleaning depot for WCC will be built.