May is "ideally placed to implement Brexit on the best possible terms for the British people", Leadsom said in a statement announcing her withdrawal.
Theresa May became the sole contender to be Britain's next prime minister on Monday after her only rival pulled out in a dramatic twist as turmoil sweeps the political scene in the wake of the Brexit vote.
Andrea Leadsom, who had come in for heavy criticism after appearing to imply that she was more qualified than May because she had children, said a lengthy leadership race would be "highly undesirable".
May is "ideally placed to implement Brexit on the best possible terms for the British people", Leadsom said in a statement announcing her withdrawal from the contest to lead the governing Conservative Party.
On a tumultuous day in British politics, Labour lawmaker Angela Eagle also launched her bid to take over the leadership of the main opposition Labour Party from veteran socialist Jeremy Corbyn.
Conservative Prime Minister David Cameron resigned after failing to persuade Britons to vote to stay in the European Union in a seismic June 23 referendum and his successor was due to be announced on September 9.
It was unclear whether May would automatically become the next prime minister or whether Conservative MPs could choose another candidate to stand against May, ensuring a contest still goes ahead.
Interior minister May, 59, who would be Britain's first female prime minister since Margaret Thatcher, launched her policy campaign earlier on Monday by promising to lead Britain out of the European Union despite having supported the "Remain" camp ahead of the referendum.
"Brexit means Brexit and we're going to make a success of it," May said in televised remarks.
"There will be no attempts to remain inside the EU, there will be no attempts to rejoin it by the back door, no second referendum," May said.
"I will make sure that we leave the European Union," said May, who has promised to begin formal talks to leave the EU by the end of the year at the earliest despite pressure from EU leaders to speed up.
'Dangerous times' for Britain -The referendum result has plunged the economy into uncertainty and Britain's two main parties, which have dominated politics for nearly a century, into turmoil.
As she announced her leadership campaign, Eagle said: "These are dark times for Labour and they are dangerous times for our country".
"Jeremy Corbyn is unable to provide the leadership that this huge task needs. I believe I can," the former shadow business secretary said, referring to the process of leaving the European Union.
"This vote was a message for millions in our country who felt that no-one had listened to them for a very long time," she said.