Graham Brady, who heads the committee running the leadership election, said May was confirmed by the party board.
Standing outside 10 Downing St. Cameron said: "We will have a new prime minister in that building behind me by Wednesday evening."
Cameron announced his resignation after failing to convince voters to remain in the EU in a June 23 referendum. May had campaigned tepidly for Britain to remain but on Monday sought to reassure those who voted "leave" that she would respect their wishes.
Leadsom, a "leave" supporter, said Britain needed stability amid the uncertainty caused by its vote to leave the European Union. She stepped down from the Conservative leadership race earlier
Monday after a weekend furor over comments in which she appeared to say being a mother gave her an advantage over May, who has no children.
Her withdrawal -- only a week after she announced she was running -- took the country by surprise. May was 120 miles away in Birmingham formally launching her leadership campaign when Leadsom spoke outside her London campaign office.
In a brief statement, Leadsom said she had concluded she lacked "sufficient support" among legislators to be leader. She said "the interests of our country are best served by the immediate appointment of a strong and well-supported prime minister."
It is the latest spin of the political whirlwind unleashed by Britain's vote to leave the EU. Cameron's resignation announcement the next day triggered the Tory leadership race. The most prominent contenders to replace him -- including "leave" campaign leaders Boris Johnson and Michael Gove -- fell one by one amid allegations of treachery and scheming.