The Brunswick Street Hub building would be home to 1,450 civil servants and represents a £118m investment into the town.
Construction of the building is timetabled to begin later this year and be completed in early 2027.
When completed, Brunswick Street will form part of a government campus of three buildings, including Feethams House and Bishopsgate House, all located within Darlington town centre.
Clive Anderson, director of capital projects at the GPA, said: “In submitting our planning application, we are a step closer to creating another highly sustainable new government hub which will boost the local economy and see a modern, inspirational and energy-efficient workplace for government departments and their staff attracted to a rewarding civil service career based in Darlington.
“The campus is enabling increased investment in the region and supporting the Government’s Levelling Up and Places for Growth agendas, creating circa 1,400 Civil Service roles and providing future growth opportunities to the North East of England.”