TfL staff is due to relocate from the property in 2015. TateHindle will be developing plans for a conversion of the Grade I listed office building into flats. The architect was selected following a tender process launched by TfL last year.
TfL said in a statement that it had considered "every potential option" for the building, including offices, hotel and residential uses. It said that a residential led development would "not only deliver the best value for fare and taxpayers, but it would also be the most suitable option for the Grade I listed building to maintain its internal and external heritage".
The building, which sits above St James underground station, was built in the 1920s and has been occupied by London Underground for more than 80 years. It was Grade II listed in 1970 and upgraded to Grade I in 2011 by English Heritage on account of its outstanding national historic and architectural interest.
TfL said it expects to submit a planning application to Westminster City Council in the autumn.