Ms Leadsom said Ms May was ideally placed to implement Brexit and offered the Home Secretary her full support.
Ms Leadsom – who had admitted she was “shattered” by the experience of intense media scrutiny since securing the second place on the ballot paper in the leadership contest – said she had decided she did not have sufficient support among MPs “to lead a strong and stable government”.
She said the country needed a new prime minister as soon as possible and Ms May was ideally placed to deliver Britain’s withdrawal from the EU following last month’s referendum.
Chairman of the Tory backbench 1922 Committee Graham Brady said there is no need to re-run the leadership contest and that Ms May is the only remaining candidate to be party leader.
He said the party must formally confirm Ms May as the new leader, but that would be much sooner than expected.
Mr Brady added that he was hoping to hold discussions this afternoon, but was unable to say whether Ms May would be confirmed as prime minister by the end of the day or the week
Michael Gove, who was eliminated from the leadership race last week, backed Ms May, saying: “We should now move as quickly as possible to ensure Theresa May can take over as leader. She has my full support as our next prime minister.”
In a statement accepting that Ms May has effectively been chosen as Tory leader, and prime minister the Home Secretary’s campaign manager, Chris Grayling, said she was “enormously honoured to have been entrusted with this task”.
Ms May, who launched her national campaign with a speech in Birmingham just moments before Ms Leadsom’s withdrawal, was travelling back to London to make a statement.
“Theresa will do everything she can to equip our country for the challenges that lie ahead,” said Mr Grayling.
Former London mayor Boris Johnson – who abandoned an expected run for the leader’s job after realising he faced competition from both Ms Leadsom and Mr Gove – also said he had “no doubt” that Ms May would make an excellent party leader and prime minister.
Downing Street sources said discussions are under way about the timing of Mr Cameron’s departure.
The handover of power to a new prime minister had not been expected to take place until after the conclusion of the ballot of 150,000 Conservative members on 9 September.
Labour election co-ordinator Jon Trickett said he was putting the whole party on general election footing.and the Liberal Democrats and Greens demanded an early election following Ms May’s “coronation”.