David Cameron has chaired his final cabinet meeting, with some "wonderful tributes" paid to the outgoing PM.
Theresa May is preparing to take over from Mr Cameron, who will hand in his resignation to the Queen on Wednesday.
Mrs May, home secretary since 2010, had been expecting a nine-week race for the Tory leadership, but rival Andrea Leadsom withdrew on Monday.
Mrs May, who has pledged to make Brexit a success, will appoint her own ministerial team when she takes office.
She says she is "honoured and humbled" to be taking over as Conservative Party leader and, therefore, prime minister.
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Speaking after Tuesday morning's cabinet, Health Secretary Jeremy Hunt said there were some "wonderful tributes" to Mr Cameron led by Mrs May and Chancellor George Osborne.
"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,
"But also huge gratitude to him for what's he achieved for the country and the way he's changed the Conservative Party," he said.
Culture Secretary John Whittingdale described the meeting as "quite emotional", saying there was "sadness" about the PM's departure, while Commons leader and Brexit campaigner Chris Grayling spoke of a "very warm sentiment around the table".
"We all recognise what a good job he's done for the country," Mr Grayling added.
By Ben Wright, BBC political correspondent
Quietly, calmly, power is passing from one prime minister to the next.
At the back of Downing Street, cardboard boxes were carried to a bright blue removal van, the Cameron family's possessions heading for a new home.
There hasn't been much time to pack. Theresa May's accelerated ascent to the premiership has hastened David Cameron's departure - his hopes of leading a five-year majority conservative government ended after one.
Sitting around the table at his final cabinet meeting were ministers who had taken opposing sides in the referendum. But this was a time for poignant tributes and thanks.
And as the team of cabinet ministers later filed out of Number 10, wondering if they would be back and in what job, one member stayed behind - Theresa May, for half an hour.
A chance perhaps, for David Cameron to hand on some advice. Only those who have been prime minister can really know what it's like.
When Mrs May emerged into the sunshine, she walked one way, hesitated, then went the other - looking for her car.
At the steps of Number 10 she gave an awkward wave for the cameras - a ritual she will have many chances to practise.
As she left to plan her new cabinet, David Cameron made his last official visit as prime minister to a free school in West London. A moment to reflect on what he had achieved and what might have been.
Mrs May - who posed briefly for photographs on her way in to Downing Street - is to appoint a new ministerial team when she takes over the reins on Wednesday.
The swift transition comes after the expected nine-week leadership campaign was truncated to just a couple of days by leading Brexit campaigner Andrea Leadsom's withdrawal from the contest.
Mrs Leadsom's surprise announcement meant Mrs May, who had been the front runner, was the only remaining candidate in the race.
After being formally declared the winner of the contest, Mrs May praised Mr Cameron for his stewardship of the party and the country and paid tribute to Mrs Leadsom for her "dignity" in withdrawing her leadership bid.
But senior Labour MP Jon Trickett has joined the Lib Dems and Green Party in calling for a snap general election.
Mr Trickett, Labour's general election co-ordinator and an ally of leader Jeremy Corbyn, said it was "crucial" to have a "democratically elected prime minister" and said he was putting the party on "general election footing".
Mrs May has rejected such demands.
BBC political editor Laura Kuenssberg said EU negotiation, controlling immigration and managing the economy were "huge issues" that would challenge Mrs May's desire for a "steady as she goes" approach.
Former chancellor Ken Clarke - who supported Mrs May in the final ballot - said the new leader and prime minister needed to "balance the party" in her cabinet appointments.
"She's got a real problem of bringing the warring wings of the party together. She'll combine her own strong personal opinions about who she wants to work with, with a desire to bring the party together," he said.
But he cautioned that the party's small parliamentary majority would not make the task "easy".
"To actually get the real head-bangers together on both sides and to see four years of government through will require some political skill… but she's pragmatic, she'll want to get on and do things," he said.
Northern Ireland secretary Theresa Villiers - who backed Mrs Leadsom in the contest - said she was sure Mrs May would "want to draw on talents from across the parliamentary party".
Asked whether Mrs May should balance the cabinet, she said: "I certainly hope that both Remain and Leave campaigners will be represented in the cabinet."
But she urged all colleagues, whatever the outcome of the reshuffle, to be "incredibly supportive" of the new prime minister, saying a "stable government" was needed.
Mrs May said she had based her leadership bid on the need for "strong, proven leadership", the ability to unite both party and country and a "positive vision" for Britain's future.
And in a message perhaps designed to reassure Brexit-supporting colleagues on Monday, Mrs May, a Remain campaigner, said: "Brexit means Brexit - and we're going to make a success of it."
Mr Cameron, who has been prime minister since 2010, decided to quit after the UK's referendum vote to leave the EU, having campaigned for the losing side.
He said Mrs May would have his "full support", describing her as "strong", "competent" and "more than able to provide the leadership" the country needs.
What happens next?
- The 1922 Committee of Conservative MPs, which is overseeing the leadership contest, has declared Mrs May the new party leader "with immediate effect"
- David Cameron says he will take Prime Minister's Questions on Wednesday and then head to Buckingham Palace and officially tender his resignation to the Queen and recommend she sends for Theresa May as his replacement
- Mrs May will then go to Buckingham Palace to see the Queen and receive her invitation to form a government
- Theresa May should then be in place as UK prime minister by Wednesday evening - it is not yet clear when the Cameron family will move out of No 10
Key dates for the new PM
- 18 July - Parliament due to vote on Trident renewal
- 19 July - Possible date for first cabinet meeting
- 20 July - First PMQs as prime minister
- 5 September - Parliament returns from summer recess
- 2-5 October - Conservative Party annual conference
- 20 October - First European Council meeting as prime minister
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