Boris Johnson is to be sworn in Wednesday as UK Prime Minister.
He was on Tuesday elected the new Conservative leader in a ballot of party members, paving the way for his appointment.
Johnson beat Jeremy Hunt comfortably, winning 92,153 votes to his rival's 46,656.
In his victory speech, Johnson, who is a former Foreign Secretary, promised to deliver Brexit, unite the country and defeat Jeremy Corbyn.
Hunt said he was very disappointed with the result, but Johnson would do a great job.
May, who is standing down after a revolt by Conservative MPs over her Brexit policy, congratulated her successor, promising him her full support from the backbenches.
US President Donald Trump also sent his congratulations to Johnson, tweeting: "He will be great."