The university has been working up its London Road project as part of ambitious plans to redevelop its main campus near the Elephant & Castle area in the capital.
The 1970s London Road building is the largest at the Southwark campus.
Its four storeys will be completely overhauled and modernised to accommodate 20,000sqm of teaching and learning resource space, including specialist multi-media areas, along with sports facilities and catering facilities.
Works include infilling two of the existing light wells to create an open plan library.
As well as the relocated library to the upper two floors, the building will house the Academy of Sport with sports hall and gym.
New brickwork, glazing and GRC cladding will be fitted to the existing building envelope to create a modern academic building.