Construction will start early next year on 46,300 square metres of commercial, retail, public realm and residential units and is scheduled to complete in 2023.
The project has been a long-time getting to site after opposition from conservationists concerned about the impact on the historic Norton Folgate area.
Kier was originally lined-up for the job after winning the pre-construction phase but was dropped by British land in the summer of 2019 when the developer went out to tender for other firms.