Mrs May, who at 59 becomes the oldest incoming prime minister since Jim Callaghan in 1976, will then return to No 10 as the country's second female prime minister, following in the footsteps of Margaret Thatcher.
In a carefully orchestrated political ballet, Cameron made his final appearance as prime minister in Parliament, turning the usually raucous prime minister's questions session into a time for praise, thanks, gentle ribbing, cheers - and a sprinkle of criticism.
Larry's been at home at 10 Downing Street since 2011 when he was recruited from Battersea Dogs & Cats Home for his ability to catch mice.
Samantha Cameron, the former prime minister's wife, has been a public figure alongside her husband.
David Cameron has signed off his final Prime Minister's Questions telling MPs: "Nothing is impossible". May arrived at the palace with her husband Philip for her private audience with Queen Elizabeth II just minutes after the Camerons left.
"Until we have served an article 50 notice, we remain a full, participating member of the EU and our ability to negotiate new trade agreements is restricted by the continued application of EU law until we have negotiated our exit from the EU", he said.
"It has been the greatest honor of my life to serve our country as prime minister over these last six years, and to serve as leader of my party for nearly 11 years", he said, accompanied by his wife Samantha and his children - 12-year-old Nancy, 10-year-old Elwen and 5-year-old Florence.
During his tribute, Mr Kinahan said the prime minister had visited Northern Ireland "often" during his six-year tenure.
But as Tory May gets ready to takeover Downing Street, one beloved resident is not moving as it was announced Larry the Cat is staying - with some bookies giving him top odds to outlast the new PM. But today the country is much stronger; our economy is immeasurably stronger.For me politics has always been about public service in the national interest.
The book included a number of details about Mr Cameron he would no doubt rather did not go into print.