Theresa May is set to become the UK's next prime minister after Andrea Leadsom pulled out of the contest to become Conservative Party leader.
The timing of the handover of power from David Cameron looks set to be after PM's questions on Wednesday.
Mrs May, 59, who backed staying in the EU, has been home secretary since 2010.
Mrs Leadsom, who campaigned to leave the EU, said the UK needed "strong and stable government" and that Mrs May was "ideally placed" to implement Brexit.
The 1922 committee of Tory MPs - which is overseeing the leadership contest - is holding talks with the Conservative Party board over formally declaring Mrs May the winner, after Mrs Leadsom dropped out.
A statement is expected from its chairman, Graham Brady, at about 17:00 BST.
Mrs May is also expected to make a public statement, at about 18:00 BST, according to BBC assistant political editor Norman Smith.
In a speech earlier on Monday setting out her leadership campaign platform, Mrs May - who rejected the argument that the next leader and prime minister had to have been someone on the winning side of the EU referendum - said: "Brexit means Brexit and we're going to make a success of it."
In her brief statement in Westminster, Mrs Leadsom - who was a leading light of the Brexit campaign - said a nine-week leadership campaign at such a "critical time" for the UK would be "highly undesirable".
A source close to the energy minister told BBC political editor Laura Kuenssberg "the abuse has been too great" for Mrs Leadsom during the contest.
Mrs Leadsom had apologised to Mrs May on Monday after suggesting in a weekend newspaper interview that being a mother made her a better candidate for the job.
Mrs Leadsom, who was flanked by some of her supporters as she read the statement, said: "Strong leadership is needed urgently to begin the work of withdrawing from the European Union. A nine-week leadership campaign at such a critical moment is highly undesirable."
She said Mrs May, the home secretary, had the support of more than 60% of Conservative MPs and was "ideally placed to implement Brexit on the best possible terms for the British people and she has promised she will do so".
Mrs Leadsom said she was "incredibly grateful" to the 84 colleagues who supported her leadership bid.
But she added: "Nevertheless, this is less than 25% of the parliamentary party and after careful consideration I do no believe this is sufficient support to lead a strong and stable government should I win the leadership election."
She said: "There is no greater privilege than to lead the Conservative Party in government and I would have been deeply honoured to do it.
"I have however concluded that the interests of our country are best served by the immediate appointment of a strong and well-supported prime minister.
"I am therefore withdrawing from the leadership election, and I wish Mrs May the very greatest success."
What happens next?
- The 1922 committee is holding discussions with the Conservative Party board to discuss confirming Mrs May as the winner
- David Cameron says he will do Prime Minister's Questions on Wednesday and then head to Buckingham Palace and officially tender his resignation to the Queen and recommend she sends for Theresa May as his replacement
- Mrs May will then go to Buckingham Palace to see the Queen and receive her invitation to form a government
- Theresa May should then be in place as UK prime minister by Wednesday evening
The leadership contest is being overseen by the 1922 committee of backbench Conservative MPs.
Its chairman, Graham Brady, said Mrs May would be formally confirmed as the new party leader as soon as the Conservative Party board had been consulted - saying there would be "no need to re-run the election".
He declined to give an exact timetable for the next steps - other than to say it would not be "nine weeks" until Mr Cameron's successor was in place.
The contest was originally scheduled to finish on 9 September.
The time between Gordon Brown winning the Labour leadership uncontested and succeeding Tony Blair as prime minister was 38 days.
Reacting to Mrs Leadsom's decision, Chris Grayling, Mrs May's campaign chief, said it showed what a "principled and decent politician she is".
Speaking outside the Houses of Parliament, he said Mrs May was "enormously honoured" to be entrusted with the task of leadership, and would make a statement later.
In a message to the party, he added: "Now is the time for us to unite... and get on with the job of securing a strong, prosperous future for our country."
Meanwhile, former London mayor Boris Johnson - who was backing Mrs Leadsom's leadership bid, said he had "no doubt" Mrs May would be an "excellent" leader and prime minister.
He said he was "encouraged" by Mrs May's statement that "Brexit means Brexit", and added: "It is vital that we respect the will of the people and get on with exploiting new opportunities for this country."
There had originally been five contenders to succeed Mr Cameron, with MPs voting in two rounds to get that number down to two - and the plan then was that the party's 150,000-strong membership would have had the final say.
Labour, the Lib Dems and the Greens are calling for a snap general election, rather than waiting for the contest scheduled for 2020 under the Fixed Term Parliaments Act.
Labour's election co-ordinator, Jon Trickett, said: "It is crucial, given the instability caused by the Brexit vote, that the country has a democratically elected prime minister. I am now putting the whole of the party on a general election footing."
Mr Farron, Lib Dem leader, said: "With Theresa May's coronation we need an early general election. The Tories now have no mandate. Britain deserves better than this."
Meanwhile, a Labour leadership contest has begun after Angela Eagle launched a bid to challenge Jeremy Corbyn for the job, saying she she could provide the leadership in "dark times for Labour" that Mr Corbyn could not.