The scheme for 20-26 Rosebery Avenue, backed by commercial developer Derwent London, involves reworking the building into new office space by extending the block by two floors.
BGY had to battle to gain planning consent due to the building's location within the Rosebery Avenue conservation area.
The 4,700m2 project was particularly sensitive as the site is adjacent to two Grade II-listed buildings, but after lengthy discussions at appeal, Islington Council planners were satisfied with the practice's designs to upgrade the building sympathetically.
BGY principal Richard Buckley said: 'We are extremely pleased that this scheme has won planning at appeal, the two-storey extension has been sensitively designed to add to the commercial appeal of what is a beautiful building in the heart of Clerkenwell.'
The project is due to start on site late this year, with completion set for mid-2008.