Home Secretary Theresa May is expected to succeed Prime Minister David Cameron after her only rival, Vote Leave campaigner Andrea Leadsom, pulled out of the race on Monday.
Launching her campaign earlier Monday, May, 59, said the country would remain fully committed to a Brexit under her leadership despite her previous opposition to leaving the EU.
"There will be no attempts to remain inside the EU ... no attempts to rejoin by the back door," May told supporters and journalists.
She said a Conservative Party under her leadership would "put ourselves at the service of working people... [and] make sure our economy truly works for everyone.
Leadsom, 53, read out a letter informing the Conservatives' election committee of her decision to withdraw her candidacy.
She cited the far greater support May enjoys among Conservative lawmakers and saying it was in everyone's interests to avoid a nine-week leadership campaign that would prolong the political and economic uncertainty that followed the June 23 Brexit referendum.
Leadsom said she believed May is "ideally placed to implement Brexit on the best possible terms."
"Business needs certainty," she said. "We now need a new prime minister in place as soon as possible."
Graham Brady, chairman of the election committee, told reporters the party will still "need to respect the process," but said a new leader would certainly be announced in less than nine weeks after Leadsom's withdrawal.
The committee now needs to "get the clear views of the Conservative Party board," Brady said. "There is no need to rerun the election."
Cameron failed to convince voters in last month's referendum on EU membership to vote against a so-called Brexit, prompting his resignation.
May supported Cameron's Remain campaign, but she insisted in her speech that "Brexit means Brexit and we're going to make a success of it."