Kier has signed a pre-construction deal in readiness to deliver the project, earmarked for Brunswick Street, after the planning application was lodged with Darlington Borough Council last month.
The Hub building would be home to 1,450 civil servants and represents a £118m investment into the town.
Construction of the building is scheduled to begin at the end of this year and be completed in early 2027.
Kier and the GPA are now set to develop the design and engage with the supply chain to prepare the way for building to begin.
Stuart Togwell, group managing director of Kier Construction, said: “Working in partnership with the GPA, we will create an exemplar building to support and create a new flagship regional hub for the government.
“Our strong regional footprint also means we will deliver the scheme through local supply chains and create employment opportunities including apprenticeships.”