Theresa May will officially step down as the leader of the Conservative Party on Friday, but will remain as prime minister until her successor is chosen.
Mrs May announced her resignation two weeks ago, saying it was a matter of deep regret that she had been unable to deliver Brexit.
Eleven Conservative MPs are vying to replace her as party leader and ultimately, prime minister.
Nominations open from 10:00 BST on Monday and close at 17:00 BST that day.
Mrs May remains acting leader while the contest takes place.
The UK was originally meant to leave the European Union on 29 March. That was then pushed back to 12 April and eventually 31 October after Mrs May failed to get MPs to approve her deal.
She announced her resignation, saying she had done everything she could to try to persuade MPs to support the withdrawal deal which she had negotiated with the European Union but it was now time for a new prime minister to try to deliver Brexit.
Leadership candidates need eight MPs to back them. MPs will then vote for their preferred candidates in a series of secret ballots held on 13, 18, 19 and 20 June.
Charles Walker of the Conservative backbench 1922 committee, which sets the rules, said on Thursday: “We are aiming to have two people by Thursday 20 June.”
The final two will be put to a vote of members of the wider Conservative Party, with a winner expected to be announced in the week of 22 July.
While the contest does not officially start until Mrs May steps down, candidates have already been jostling for position.