Cameron, who has been premier for six years, will say his goodbyes at his last question-and-answer session in parliament before tendering his resignation to Queen Elizabeth II at Buckingham Palace.
The monarch will then call on May, interior minister in the outgoing government, to form a cabinet.
The newly-anointed prime minister is expected to begin announcing her ministerial choices before the day is out, including a Brexit minister in charge of leading negotiations with the EU on a new relationship.
Finance minister George Osborne, who fought hard to remain in the EU, is expected to lose his job, with May sharply criticising his economic legacy earlier this week.
Women are expected to secure several top jobs, with current energy minister Amber Rudd and international development minister Justine Greening tipped for lead roles along with foreign minister Philip Hammond and Brexit campaigner Chris Grayling, who is leader of the House of Commons.
Johnson among cabinet hopefuls
Friends of former London mayor Boris Johnson told The Telegraph newspaper he also hoped to play a “significant role”, two weeks after he dramatically withdraw from the race to succeed Cameron at the last minute.
Investors will be watching May’s first days in office closely but with greater optimism after the pound, which fell by up to 15 percent against the dollar and the euro after the Brexit vote, began to rebound.
EU leaders have said they expect May to move quickly to formalise Britain’s divorce from the union.
In a sign of their anxiousness to move ahead, French President Francois Hollande, German Chancellor Angela Merkel and Italy’s Prime Minister Matteo Renzi will hold a summit in August on the Brexit vote, the French presidency said Wednesday.
May has indicated however she will not be rushed into triggering the formal procedure for Brexit. The steely 59-year-old vicar’s daughter will be Britain’s only second female premier after Margaret Thatcher, with whom she is now inevitably being compared.
She faces a stiff task in bridging Conservative Party divisions and dealing with a potential economic downturn.
Her other mammoth challenges include keeping pro-EU Scotland from bidding for independence in order to stay in the 28-nation bloc, and weaving new trade and diplomatic alliances with the US, India and other powers to prepare for a post-EU future.
May campaigned, albeit quietly, with Cameron for Britain to stay in the EU and she will have to convince eurosceptics within her party and the country at large that she has no intention of backtracking on the June 23 vote.
“Brexit means Brexit — and we’re going to make a success of it,” the politician reputed to be a tough negotiator has said.
After six years in office, Cameron announced he would resign the day after the referendum. He will chiefly be remembered for organising a ballot aimed at stopping his party “banging on about Europe” and then spectacularly failing to clinch it.
He sought to deflect that criticism in an interview with the Daily Telegraph on Wednesday, saying: “As I leave, I hope people will see a stronger country, a thriving economy and more chances to get on in life.
May’s bid for his job accelerated as key proponents of Britain’s EU withdrawal, including Johnson, stepped back or were vanquished in a head-spinning round of political bloodletting.
The vote exposed deep inequalities in British society, which May has vowed to address, and plunged the opposition Labour party in turmoil.
On Wednesday, Owen Smith became the second Labour MP to announce a bid to try to oust embattled party leader Jeremy Corbyn, who is resisting pressure to resign over his lacklustre campaigning for Britain to remain in the EU.
May has been a tough-talking interior minister for the past six years and is something of an unknown quantity internationally, although she has received ringing endorsements from party colleagues and a normally sceptical British tabloid press.
The daughter of a Church of England pastor, May is a cricket fan with a sober, well-mannered demeanour who lists her hobbies as cooking and walking.
She is well liked in and around Maidenhead, the well-to-do commuter town west of London that she has represented in parliament since 1997. “She will get this country back on its feet,” said 69-year-old Jim Charlesworth, a neighbour of May and her banker husband Philip.
Martin Trepte, editor of the Maidenhead Advertiser, the local newspaper, said: “She’s a mature, grown-up, no-nonsense politician. She knows her stuff.” She shows a flash of flamboyance with a colourful shoe collection — particularly her leopard-skin heels.