GDS has pre-let the top two floors of the building - 53,700 square feet - paying an initial rent of £2.8m per annum.
The move from GDS is part of the government's plan to situate the service near the tech firms currently populating east London (The White Chapel Building is in E1).
The building is now 75 per cent pre-let, Derwent London said. Perkins + Will, Reddie & Grose, The Shipowners' Club and Unruly Media have already agreed to take space in the Whitechapel office block.
All but one of the lettings were agreed after the EU referendum.
Cushman & Wakefield, BNP Paribas Real Estate and Colliers International acted as agents for Derwent London.
Ben Gummer, minister for the Cabinet Office and paymaster general, said: "With more money and improved offices, GDS can accelerate their efforts to transform and improve public services right across the UK."
John Burns, chief executive of Derwent London, said: "The arrival of GDS is another great addition to The White Chapel Building which now hosts an exciting mix of occupiers across the tech and professional services sector."