A new prime minister will be in Downing Street by the end of July, according to the Conservative Party.
A statement from the party's chairman and the backbench 1922 Committee said nominations for the leadership would close in the week starting 10 June.
MPs will then whittle the candidates down to two by the end of June, before party members vote for their choice ahead of Parliament's summer recess.
The statement praised Theresa May for her "dedication, courage and tenacity".
Mrs May announced earlier that she will quit as Conservative leader on 7 June, but would continue to serve as PM while a leadership contest takes place.
In the joint statement from Tory MPs Brandon Lewis, Dame Cheryl Gillan and Charles Walker, they said their focus would be on "facilitating a full, fair and frank debate and contest".
"We are deeply conscious that the Conservatives are not just selecting the person best placed to become the new leader of our party, but also the next prime minister of the United Kingdom," they said.
"We will therefore propose that the leadership election and hustings involve opportunities for non-members and people who may not yet vote Conservative to meet the candidates and put their questions to them too."
Four MPs have announced they will run for the leadership so far: Foreign Secretary Jeremy Hunt, former foreign secretary Boris Johnson, former work and pensions secretary Esther McVey and International Development Secretary Rory Stewart.
More than a dozen others are believed to be seriously considering entering the contest.
Sir Graham Brady has stood down as chair of the 1922 Committee, having been "urged" by MPs to stand for the leadership. He said he was "considering the approaches... and will make a decision in due course".
Labour leader Jeremy Corbyn said whoever takes over as prime minister should call an "immediate" general election to "let the people decide our country's future".
How will the next PM be chosen?
The Conservative Party will be in charge of picking the next prime minister through their own leadership contest.
Any Tory MP can stand, as long as they have the backing of two parliamentary colleagues.
When nominations have closed, all the party's 313 MPs will vote for their preferred candidate.
After the first vote, the candidate who comes last will be struck from the list, and MPs will get to vote again.
This process will continue until they have whittled down the candidates to just two.
After a round of hustings - allowing the leadership contenders to make their case and for people to question them - the final decision will be put to Conservative Party members.
Whoever those 124,000 people vote for will then become prime minister.
When will it happen?
- 7 June - Theresa May stands down as party leader
- Week commencing 10 June - Nominations for leadership candidates close
- 30 June - Expected deadline for rounds of votes to conclude
- July - Campaign hustings around the UK and party members' vote
- By summer recess (expected at the end of July) - New leader announced and becomes prime minister