Mrs May arrived at Downing Street from Buckingham Palace, where she officially accepted the Queen's invitation to form a new government.
Before heading to the audience with the queen, Cameron said outside the prime minister's residence at 10 Downing Street that it was the "greatest honor" of his life to serve as prime minister.
Cameron was speaking during his final appearance in parliament as prime minister, before he tenders his resignation to Queen Elizabeth II and May takes over later Wednesday.
He said it had been the "greatest honour of my life" to serve as prime minister over the last six years and as Tory leader for nearly eleven years.
The only other woman to be prime minister of Britain is Margaret Thatcher, who held power from 1979 to 1990.
Then, after a rousing speech defending his government's legacy, he and his family left his home at 10 Downing Street for the last time and made the short drive to Buckingham Palace. "And when I say willingly you on, I don't just mean willing on the new prime minister at this despatch box, or indeed just willing on the front bench defending the manifesto that I helped put together", Cameron said in his address to the House of Commons.
But Cameron drew praise from an old adversary, with European Commission President Jean-Claude Juncker saying he would miss the British leader.
But she said that for her, being a Unionist also meant preserving the bonds between all the country's citizens "whoever we are and wherever we are from".
May had advocated waiting until the end of this year to invoke Article 50 of the Lisbon Treaty, which sets the rules for a nation leaving the European Union, but many British and European Union politicians have urged her to move more quickly.
"UK%27s+Leave+Vote+in+EU+Referendum" Cameron resigned immediately after the outcome of June's referendum on the UK's membership to the EU in which 51.9 % of voters had EU+Referendum" supported Brexit.
At Buckingham Palace, the queen asked May, who had been home secretary, to form a government.
Cameron stepped down after Britons rejected his entreaties to stay in the European Union, sending shock waves across the 28-nation bloc.
May had campaigned for Britain to "Remain" but since the vote, she has said, "Brexit is Brexit" and is striving to make it a success.
She will name her own frontbench team after taking office.