The Homes and Communities Agency with site owner Defence Estates selected Grainger to deliver the Aldershot Urban Extension plan last year.
At 150 hectares of development land, it ranks as one of the largest brown field sites in the country. As well as 3,850 new homes, of which over a third would be affordable, the plan is to build two new schools
Six-listed buildings including the large Cambridge Military Hospital complex and Headquarters 4th Division will be refurbished to create homes.
Grainger also sought permission to demolish the Duchess of Kent Barracks.
It plans to develop the site in phases over 15 years, with work on phase one starting in early 2014.
Andrew Lloyd, Chief Executive of Rushmoor Borough Council, said: “The Aldershot Urban Extension is one of the most important developments for Aldershot and the wider area in many years, as it will allow the town to grow for the first time in nearly a century, bringing new people to the area.
“With nearly 4000 new homes, schools, green space and community facilities, the development will provide more choice for local families and for new residents to put their roots down in Aldershot.
“We are also particularly pleased that it will protect and build upon the area’s military heritage and green open space, which is very dear to the hearts of local people.”