She arrived at the Palace by ministerial vehicle, having set off from the House of Commons only after receiving the signal that Mr Cameron's resignation had been accepted by the Queen and that he had advised her to appoint Mrs May in his place.
Earlier Wednesday, Cameron took questions from members of Parliament at the House of Commons, which ended in a standing ovation from lawmakers.
Other cabinet decisions May made Wednesday include Amber Rudd as home secretary, and the retention of Michael Fallon as defense secretary. Though admitting he had "not got every decision right" while in office, Cameron affirmed his belief that "today, our country is much stronger" and praised May for her "strong and stable leadership".
Johnson said on his appointment: "We have a massive opportunity in this country to make a great success of our new relationship with Europe and with the world".
May's first address as prime minister, delivered outside 10 Downing Street on Wednesday, indicated her resolve to confront the domestic forces that motivated Brexit.
One of the more cheerful exchanges took place between Cameron and Labour leader Jeremy Corbyn.
"Following the referendum we face a time of great national change", the 59-year-old told reporters, flanked by her banker husband, Philip.
"I was the future once", Cameron quipped as he left office.
Cameron also took a moment to discuss the Downing Street cat, Larry, who is being left behind to keep working as the resident mouse-catcher.
France's foreign minister has branded his British counterpart, incoming Foreign Secretary Boris Johnson, a liar.
David Cameron will be appearing before Parliament as prime minister for the last time before handing over to successor Theresa May. He says Obama is confident the US will keep working to strengthen relations "irrespective of specific personalities". "I will miss the barbs from the opposition".
Surrounded by his family, he thanked his three children and his wife Samantha, who he described as the "love of my life", who has "kept me vaguely sane".
The BBC's royal correspondent Nicholas Witchell said the private audience was likely to be a short one, potentially about 20 minutes.
May had a phone call late Wednesday with German Chancellor Angela Merkel, who invited her to visit, followed by calls with the French and Irish leaders, a Downing Street spokeswoman said.
A career politician, Theresa May is the first woman to hold the office since Margaret Thatcher in 1990. "And I'm confident the next president will be able to work with her, as well".
Mrs May, who was declared the victor of the Tory leadership contest following her rival Andrea Leadsom's withdrawal, is now set to announce her new cabinet over the next two days, with half the posts set to be taken by female MPs.
Removal vans were spotted outside Downing Street on Tuesday, as Mr Cameron's ministers paid tribute to him in his final cabinet meeting.
The vote to leave the European Union roiled global stock markets and sent the pound to a 31-year low in the immediate aftermath.
Germany's foreign minister says he hopes new British Foreign Secretary Boris Johnson will want to maintain a "sensible relationship" with the European Union.
However, on Monday the only other contender, Andrea Leadsom, dramatically dropped out of the race resulting in Mrs May receiving the keys to Number 10.