Theresa May will become Britain's prime minister on Wednesday after rival Andrea Leadsom abruptly terminated her short-lived leadership campaign.
Mrs May will succeed David Cameron, who announced he was stepping down after Britons voted last month to quit the European Union.
"I am honoured and humbled to have been chosen by the Conservative Party to become its leader," said Mrs May.
She favoured remaining in the EU but has made clear there is no going back on the result of the referendum.
"Brexit means Brexit, and we're going to make a success of it."
Earlier, David Cameron told reporters in front of his 10 Downing Street residence that he expected to chair his last cabinet meeting on Tuesday and take questions in parliament on Wednesday before tendering his resignation the Queen.
"So we will have a new prime minister in that building behind me by Wednesday evening," he said.
Britain's planned withdrawal has weakened the 28-nation bloc, created huge uncertainty over trade and investment, and shaken financial markets.
In a speech earlier in the day in Birmingham, Mrs May said there could be no second referendum and no attempt to rejoin the EU by the back door.
"As prime minister, I will make sure that we leave the European Union," she said.
Theresa May will become Britain's second woman prime minister after Margaret Thatcher.
She and Mrs Leadsom had been due to contest a ballot of grassroots Conservative party members, with the result to be declared by 9 September.
But in a day of dramatic political developments, Mrs Leadsom unexpectedly pulled out of the contest, after a campaign dogged by comments about her rival's lack of children and questions about whether she had exaggerated her CV.
She had been strongly criticised over a newspaper interview in which she appeared to suggest that being a mother meant she had more of a stake in the country's future than Mrs May, who has no children. Some Conservatives said they were disgusted by the remarks, for which Mrs Leadsom later apologised, while others said they showed naivety and a lack of judgement.
Mrs Leadsom told reporters she was pulling out of the race to avoid nine weeks of campaign uncertainty at a time when strong leadership was needed. She acknowledged that Mrs May had secured much greater backing in a vote of Conservative members of parliament last week.
- Reuters / BBC