Mr Cameron will face his last Prime Minister’s Questions in the Commons, before heading to Buckingham Palace to tender his resignation to the Queen.
He told the Daily Telegraph: “As I leave today, I hope that people will see a stronger country. It has been a privilege to serve the country I love.”
After taking office, Mrs May will set about naming her own frontbench team.
The current home secretary, 59, was the only remaining candidate in the Conservative leadership contest following Andrea Leadsom’s withdrawal on Monday.
The contest began when Mr Cameron, who has been prime minister since 2010, announced he would step down after losing the EU referendum in June.
Mr Cameron told the Telegraph: “I came into Downing Street to confront our problems as a country and lead people through difficult decisions so that together we could reach better times.
“As I leave today, I hope that people will see a stronger country, a thriving economy, and more chances to get on in life.”
At midday Mr Cameron, who has said he plans to continue as MP for Witney in Oxfordshire, will face Prime Minister’s Questions for the 182nd and final time as PM – his 319th in total as Tory leader.
Later, after the PM has tendered his resignation to the Queen, Mrs May will have her own visit to Buckingham Palace, when she will accept the monarch’s offer to form a new government.
She will return to No 10 as the country’s second female prime minister, following in the footsteps of Margaret Thatcher.
- David Cameron held office for six years, 62 days
- This makes him the UK’s 22nd longest-serving prime minister
- Aged 49, he will be the youngest PM to leave office since the Earl of Roseberry in 1895
- Theresa May becomes the oldest incoming prime minister since Jim Callaghan in 1976
Removal vans were spotted outside Downing Street on Tuesday, as Mr Cameron’s ministers paid tribute to him in his final cabinet meeting.
“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.
The swift transition of power comes after the expected nine-week leadership campaign was truncated to just a couple of days by leading Brexit campaigner Andrea Leadsom’s surprise withdrawal.
Image copyrightPAImage captionThe Camerons are thought likely to head to their Oxfordshire home after leaving Downing StreetImage copyrightGETTY IMAGESImage captionA removal van was seen arriving in Downing Street on Tuesday
Mrs May, who backed a vote to remain in the EU, will unveil her full ministerial team over the next couple of days, with the focus on the key positions of chancellor and foreign secretary as well who will be put in charge of leading the Brexit negotiations.
She is expected to promote a number of women to senior positions, with International Development Secretary Justine Greening and Energy Secretary Amber Rudd among those likely to get upward moves.
Asked her about her prospects, Ms Rudd told reporters: “I haven’t been told anything yet so I’m just going to get on with my day job”.