The Swiss duo has lodged the plans with Southwark council in the hope that they will be approved in the first half of next year.
The designs are part of a strategy to open up the Tate to the south, giving Southwark a sense of ownership of the gallery.
It is hoped that it will help trigger a cultural quarter stretching down to Elephant and Castle, with resulting regeneration benefits for the deprived borough.
The new building, which Tate bosses hope will be completed in time for the 2012 Olympics, will include more space for contemporary art, especially photography, film, video and performance.
The plans also include performance spaces, a sequence of exceptional new spaces for education, a lounge and skills-development area for young people, spaces for schoolchildren and families, and a new public roof terrace.
There will also be the ubiquitous restaurants, cafés shops and offices.