It will build almost 200 new council homes, a nursery, community centre and retail space and was appointed under an intensive two-stage tender using the Pagabo framework.
The Lakes Estate is located at the southernmost end of Milton Keynes, on the outskirts of Bletchley and ranks in the top 10 most deprived areas in England for crime, income and health deprivation.
The project is being funded by the city council’s investment of almost £70m and being topped up by a grant of just under £15m from Homes England.
Jonathan Hall, Managing Director of Graham’s Building South division, said: “We are delighted to be on site and look forward to building new homes and facilities that will enhance the wellbeing and vitality for the residents and local community.”