As a partner in the Solutions 4 Brunswick consortium, the firm with Contour Homes and Mears will transform the Brunswick area, building 522 new homes as well as new community facilities.
Mears will refurbish a further 653 homes and provide ongoing facilities management services under the project.
Additionally, extensive infrastructure works and remodelling will be carried out as well as building an Extra Care centre and shops.
S4B beat rival bidder Fern Consortium, made up of Harvest Housing and Gleeson.
The redevelopment plans were postponed for several years since funding for the project was agreed by the HCA under its housing PFI programme in August 2007.
It was one of 13 housing PFI projects that the coalition government said it would support subject to a value-for-money review.
Galliford Try Chief Executive Greg Fitzgerald said: “We are delighted to have been part of the winning bid for such a significant project for the city.
“This award is a further demonstration of our strength in regeneration, and our ability to successfully partner with local councils across the country to deliver the housing and facilities that communities need.”