His decision clears the way for enabling work to start straightaway on the 347,000 sq ft regeneration scheme near to Spitalfields Market.
The developer’s plans ran into fierce opposition from local conservationists keen to protect the character of the historic Norton Folgate neighbourhood on the City fringe.
Johnson over-ruled Tower Hamlets Council, which had previously rejected the controversial scheme.
British Land plans to refurbish several existing derelict warehouse buildings and build new blocks on vacant sites to create mainly office space along with 13 shops and 40 flats.
The scheme also includes two new areas of public space, totalling 15,000 sq ft.