The decision is a big lift for Gleeson and Galliford Try which are battling it out to secure the contract and have been on tenterhooks to hear the outcome of the value-for-money assessment in Whitehall.
Manchester City Council can now move forward and choose a preferred bidder to run the PFI scheme. Work would then start early in 2013.
The Brunwick plan will see 500 homes built and 650 council houses refurbished.
Plans also include a new shopping area and a 60-bed sheltered accommodation facility.
Fern Consortium: Harvest Housing and builder Gleeson
Solutions 4 Brunswick: Contour Housing, builder Galliford Try, housing refurb Mears
The redevelopment plans have been 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.
Cllr Jim Battle, deputy leader of Manchester City Council, said: “This announcement takes us a step closer to a new Brunswick, and although we still face a number of hurdles, this is a welcome announcement that gives some light at the end of the tunnel for residents who have waited years for these plans.”