In a video to his department’s civil servants, Mr Sunak said that after “a lot of thought and energy”, the new economic campus would be in the north east market town.
Mr Sunak said he was “really excited” about the decision, according to the recording of the message which has been shared on social media.
Civic leaders across the North had made overtures in recent weeks for the Chancellor to send Treasury jobs their way.
Darlington was among the favourite places for the move, with Bradford, Leeds and Newcastle also thought to be under consideration for the plan.
Tees Valley’s Tory elected mayor Ben Houchen said last month that Darlington would be a strong option as it would represent a move away from the metropolitan cities to the north and south of the town.
He said last month: “Now is the time for the Chancellor to be at his bravest, for him to face down the anonymous Sir Humphreys within the Treasury who think we don’t have enough culture to be home of the Government’s more important and powerful department.”
Mr Sunak’s huge Richmond constituency in North Yorkshire lies south of Darlington, which has strong transport links and voted Tory at the 2019 general election.
Karl Pemberton of the Institute of Directors said: “This news is one of the most important announcements for the North East in decades.
The chair of the North East (Tees) branch added: “This will help ‘level up’ our area. Where the Government leads others should follow.”
Along with senior civil service, government Ministers, including the Chancellor, will be expected to spend a significant amount of time at the new headquarters. It will be based at a site in the town centre which has been identified but not yet made public.
Debbie Francis, City Executive for the North at Arcadis and board representative to the Northern Powerhouse Partnership, said: "This is a vote of confidence in North.
"I hope moving parts of government to our great Northern towns and cities acts as an incentive for other organisations and businesses to follow suit, in part or in full. It will have a greater impact on stimulating economic growth than the direct employment of any government jobs themselves.
"We must still ensure real powers and funding are devolved to metro mayors and local leaders to deliver the Government’s levelling up agenda but this is certainly a step in the right direction."