He was due to present his resignation to the queen at Buckingham Palace at about 5pm.
During her two-day reshuffle, Mrs May sacked 10 of Mr Cameron's closest allies.
Cameron also gave all but a guarantee to European Union citizens living in Britain that they would not be forced to leave the country when Britain leaves the bloc.
But he had some final advice for May, his long-time interior minister who was sitting beside him.
There is also speculation that May, Britain's second female prime minister - after Margaret Thatcher - will boost the number of women in top posts.
May has indicated however that she will not be rushed into triggering the formal procedure for Brexit.
She is expected to make her first speech as Prime Minister outside Downing Street, where she will outline her priorities for the new administration.
However the mood in the House was uncharacteristically jovial.
In a direct message to voters, she said: "I know you are working around the clock, I know you are doing your best and I know that sometimes life can be a struggle".
The SNP's Carol Monaghan (Glasgow North West) also laid in to the legacy Mr Cameron was leaving for Scotland - but her words were almost drowned out by loud groans from the Conservative benches.
Prime Minister's questions is usually a rowdy event, involving combative exchanges between the prime minister and the leader of the main opposition Labour Party.
"We can be tough and test our leaders perhaps more than other countries but that's something we should be proud of and keep at it".
"We got on with it. They haven't even decided what the rules are yet", he said, drawing roars of support from his side of the chamber.
"If they ever got into power it would take them about a year to work out who would sit where".
"There are many awesome moments in this job but that was one of my favourites".
"There was a feeling across the cabinet of great pride at what David Cameron has achieved over the last six years, sadness that it has ended, in a way, perhaps much quicker than people thought", said Health Secretary Jeremy Hunt.
Respondign to the media reports, Cameron said: "The rumour that somehow I don't love Larry, I do".
He took the opportunity to trumpet his government's achievements in generating one of the fastest growth rates among Western economies, chopping the budget deficit, creating 2.5 million jobs and legalizing gay marriage.
But, he pointed wistfully to the capricious winds of politics that had abruptly ended his career, saying, "I was the future once".
"In a different way, I have seen that same spirit of service in the awesome contributions of countless volunteers in communities up and down our country who are making our society bigger and stronger", he said.