The scheme, which will create 273 homes and 33,000m2 of office space, was only submitted for planning in February (Make aims for £1 billion overhaul of central London hospital) and has now been approved unanimously by Westminster City Council's planning committee.
Interior design company Candy & Candy will be leading the fit-out of the scheme, which has been dubbed Noho Square.
Speaking for Project Abbey (Guernsey), Christian Candy, also a partner in Candy & Candy, said: 'It is a remarkable achievement to have gained planning approval for such a major scheme in such a short amount of time. This is in no small way due to the efforts of the world-class team involved.'
Shuttleworth added: 'The key driver behind our design has been the need to open up the site and transform it into a dynamic new urban focal point that combines world-class architecture with the creation of a generous new public space - the first such amenity in this area of London.'