The two women had been due to contest a ballot of around 150,000 Conservative party members, with the result to be declared by Sept. 9, but the shock announcement opens the way for May to take over much sooner.
Leadsom, who has no cabinet experience, was barely known to the British public until she emerged as a prominent voice in the successful campaign for Britain to leave the European Union.
She had been 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 May, who has no children.
Leadsom read out a statement to reporters in which she said she was pulling out of the race because a nine-week leadership campaign was highly undesirable at such a critical time. She acknowledged that May had secured overwhelming backing in a vote of Conservative members of parliament last week.
"Strong leadership is needed urgently to begin the work of withdrawing from the European Union," Leadsom said.
"I have ... concluded that the interests of our country are best served by the immediate appointment of a strong and well supported prime minister. I am therefore withdrawing from the leadership election and I wish Theresa May the very greatest success. I assure her of my full support."
May, 59, who has served as interior minister for the past six years, is now set to become Britain's second female prime minister after Margaret Thatcher.
In a speech earlier today she set out her vision for the economy, calling for "a country that works for everyone, not just the privileged few".
"In the coming weeks I will set out (how) to take our economy through this period of uncertainty, to get the economy growing strongly across all parts, to deal with Britain's long-standing productivity problem, to create more well-paid jobs, to negotiate the best terms for Britain's departure from the EU and to forge a new role for ourselves in the world," May said.
May favoured the 'Remain' side during last month's referendum campaign. But she repeated her new mantra that "Brexit means Brexit", saying 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.
"The British people were given their opportunity to vote on this... They've given us a very clear message, and I think we respond to that message and we do what the British people have asked us to."
The 52-48 percent vote to quit the EU after 43 years of membership has shaken financial markets because the complex divorce process creates huge uncertainty for business, trade and investment.
It has thrown both Britain's major political parties into upheaval.
Minutes before Leadsom's announcement, opposition Labour lawmaker Angela Eagle said she would challenge Jeremy Corbyn for the leadership of the party.
Corbyn was elected last year with overwhelming support from grassroots Labour activists. He has ignored a vote of no confidence from the party's lawmakers, saying he has a responsibility to carry out that mandate.