The Department for Exiting the European Union (DExEU) will be closed down on 31 January - Brexit deadline day.
The government department, led by Brexit Secretary Stephen Barclay, oversaw negotiations between the UK and EU on the exit and future relationship.
The exit deal is now contained within a bill, expected to pass Parliament with the Conservatives' 80-strong majority.
Staff were told about the closure on Thursday, but the PM's spokesman said they would help them find jobs.
A statement from No 10 said: "The Department for Exiting the European Union will be wound up once the UK leaves the EU on the 31 January.
"DExEU staff have been spoken to today. We are very grateful for all their work and we will help everyone to find new roles."
The bill to implement the PM's Brexit deal has been formally presented to the Commons, and MPs will hold an initial vote on it on Friday.
Detailed scrutiny of the legislation is then expected to take place early next month, before the bill is sent to the House of Lords.
The Brexit department was set up by former Prime Minister Theresa May in 2016 in the wake of the referendum result.
DExEU has had three Brexit secretaries in its three years - starting with David Davis, who resigned in 2018 in disagreement with Mrs May's plan to leave the EU.
He was followed by the now-Foreign Secretary Dominic Raab, who also resigned four months later over Mrs May's approach.
Mr Barclay took over in November 2018 and was kept on by Mr Johnson after he took over in No 10 last summer.
A former advisor to the department, Raoul Ruparel, said closing down DExEU was the "right decision" and "most sensible way to proceed".
However, he warned the expertise built up by the staff was "still very necessary".
Mr Ruparel, who also advised Mrs May on Europe, added: "I hope this will be maintained and those civil servants who want to go off to work on other issues will be supported."