Mrs May is already facing calls to hold a snap general election
Theresa May says she is "honoured" and "humbled" to be the new Conservative leader as she prepares to take over from David Cameron as British prime minister on Wednesday.
At lunchtime, shortly after a key campaign speech by the Home Secretary, her only rival in the Tory leadership race, Andrea Leadsom, withdrew.
Mr Cameron was then whisked back from an air show in Hampshire to Downing Street.
Just before 4pm, Mr Cameron came out of Number 10 and told the waiting media that he will do a final 'Prime Minister's Questions' on Wednesday and then see the Queen to resign.
This evening, Mrs May was confirmed as leader of the Conservative party and then, surrounded by her supporters at Westminster, she paid tribute to her rival candidates in the race.
The Maidenhead MP, who will be Britain's second female prime minister, said Mrs Leadsom had shown "dignity", and also expressed her gratitude to Mr Cameron.
One of her first big tasks as PM will be negotiating the UK's withdrawal from the European Union after last month's referendum.
The prime minister designate, who backed staying in the EU, said: "Brexit means Brexit and we will make a success of it."
Mrs May, 59, said she wanted to "negotiate the best deal for Britain" and "forge a new role for ourselves in the world".
And she said she wanted to reunite the nation and "give a strong new positive vision for the future of our country... that works not for the privileged view but that works for everyone of us".
She added: "We are going to give people more control over their lives. That is how, together we will build a better Britain."
The outgoing prime minister, who announced last month he was resigning after losing the EU referendum, told reporters he was "delighted" that Mrs May would be his successor, describing her as "strong" and "competent".
He said: "She is more than able to provide the leadership that our country is going to need in the years ahead and she will have my full support.
"With these changes we don't need to have a prolonged period of transition so tomorrow (Tuesday) I will chair my last cabinet meeting."
Mrs May was later confirmed as the new Tory leader by the chairman of the party's 1922 backbench Committee, Graham Brady.
Mrs Leadsom, 53, said she was pulling out of the leadership contest shortly after apologising to her rival after appearing to suggest the fact that she was a mother gave her the edge over the childless Mrs May.
The junior energy minister and Brexit supporter said a nine-week leadership campaign to succeed Mr Cameron at such a critical time for the UK would be "highly undesirable".
Mrs Leadsom said Mrs May was ideally placed to implement Brexit and offered the Home Secretary her full support.
Mrs May has also received the backing of leading Brexit supporters Michael Gove and Boris Johnson, and also pro-EU Chancellor George Osborne.
Mrs Leadsom's announcement she was quitting the race came a little more than an hour after Mrs May launched her national campaign in Birmingham.
She finished top in the MPs' ballot last week with 199 votes to Mrs Leadsom's 84.
Mr Cameron's departure had not been expected to take place until after the end of a ballot of 150,000 Conservative members on a new leader on 9 September.
There have been demands from Labour and the Liberal Democrats for Mrs May to call a snap general election.
Labour election co-ordinator Jon Trickett has said he is putting the whole party on a general election footing, on the same day Angela Eagle launched a bid to get rid of leader Jeremy Corbyn.