Southwark Council approved the £70m scheme for a glass and aluminium-clad building after the developer resubmitted its plans for the site on the south bank of the Thames.
Great Portland Estates aims to start construction work on the 80m high building later this year so that the 180,000 sq ft of offices are ready for tenants in 2013.
The building, designed by Allford Hall Monaghan Morris, is a revised version of a scheme which received permission in 2007.
The site has remained dormant for three years after original buildings were demolished.