Boris Johnson: May bidding farewell before new PM takes office
Theresa May has delivered a farewell speech in Downing Street before tendering her resignation to the Queen.
She wished new Prime Minister Boris Johnson and his government well, adding: "Their successes will be our country's successes."
Earlier, Mrs May faced MPs' questions for the final time and looked visibly emotional as she left to applause.
Mr Johnson will speak outside No 10 too, before announcing several senior cabinet appointments.
He is expected to use the opportunity to increase the number of women in full cabinet positions and boost the representation of ethnic minorities.
During his journey to Buckingham Palace to accept the Queen's invitation to form a government, Mr Johnson's car was briefly held up by protesters from Greenpeace, who formed a human chain across The Mall.
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Mrs May gave her final speech in Downing Street - her husband Philip alongside her - before heading to Buckingham Palace.
She said serving as prime minister had been "the greatest honour" and thanked all those who had worked with her.
"This is a country of aspiration and opportunity, and I hope that every young girl who has seen a woman prime minister now knows there are no limits to what she can achieve."
Mr May was briefly interrupted by a protester shouting "Stop Brexit!" but responded by saying: "I think the answer to that is - I think not."
A short time earlier, at her final PMQs, Mrs May said she would continue as a constituency MP and was "looking forward to asking the questions" in future.
She said she was happy to hand over to a successor committed to delivering Brexit and creating "a bright future for this country".
A number of MPs took the opportunity to praise her commitment to office and her achievements on issues like modern slavery, mental health and getting more women into politics.
Labour leader Jeremy Corbyn acknowledged Mrs May's "respect for public service", but criticised her record on the economy, homelessness and Brexit.
He asked whether she would consider joining him "in opposing the reckless plans of her successor".
She, in reply, listed what she felt were her successes, including school improvements, more employment and greater home ownership.
"At its heart, politics isn't about exchanges across these despatch boxes, nor about eloquent speeches or media headlines," she said. "It is about the difference we make every day to the lives of people up and down this country."
In a parting shot at Mr Corbyn, she added: "As a party leader who has accepted when her time was up, perhaps the time is now for him to do the same."
Former London mayor Mr Johnson won a decisive victory over Foreign Secretary Jeremy Hunt in a ballot of Tory members - gaining a 66.4% total share of the vote.
Conversations are said to be "ongoing" between Mr Hunt and Mr Johnson about the foreign secretary's next role.
The BBC's Laura Kuenssberg says Mr Johnson's choice of his top team is critical in his efforts to bring the warring factions of his party together.
Mr Johnson is resolute that his leadership rival should not stay on at the Foreign Office, but Mr Hunt is firm that he won't accept anything less than his current role - or becoming home secretary, chancellor or deputy prime minister - and considers other moves a demotion.
Our political editor says it is a risky decision for the new PM - forcing Mr Hunt out would be a bad move in terms of uniting the party, but giving in to his refusal to budge is a challenge to his authority.
Another key decision Mr Johnson faces is who will take over at the Treasury as chancellor.
The incumbent, Philip Hammond, handed in his resignation to Mrs May, saying the new PM should be free to choose someone "fully aligned" with his views on Brexit.
Those said to be in the frame to replace him include current Home Secretary Sajid Javid, former Brexit Secretary Dominic Raab and Liz Truss, Mr Hammond's deputy at the Treasury.
Meanwhile, Dominic Cummings, the former chief of the Vote Leave campaign, is expected to become a senior adviser to the new prime minister.
David Frost, a former ambassador and senior official at the Foreign Office, will be appointed as a key negotiator on Brexit.
After his victory, Mr Johnson said his priorities were to deliver Brexit, unite the country and defeat Labour leader Jeremy Corbyn.
Former Prime Minister David Cameron tweeted his congratulations to the new PM and wished him well for the "great privilege and responsibility" to come.
All the makings of a disaster?
Boris Johnson's political inheritance has all the makings of a disaster.
He has no Commons majority. There is no mandate from the general public - remember this election has only been decided by Tory members.
There are policy problems everywhere in sight, whether that's trying to solve the conundrums of Brexit with a reluctant EU and a divided party, or trying to address deep-seated problems at home.
And just as among his fans there is genuine excitement that he will, at last, be in Number 10, there is scepticism and disbelief from the opposition parties, and double-sided concerns in his own party.
Sweeping changes are expected in the wider cabinet, with a number of other ministers, including Justice Secretary David Gauke and Development Secretary Rory Stewart, having said they cannot serve under Mr Johnson due to his determination to leave the EU, with or without a deal, on 31 October.
Those tipped for promotion include Employment Minister Alok Sharma and Local Government Minister Rishi Sunak.
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Priti Patel could return to the cabinet less than two years after resigning as international development secretary over a row over unauthorised meetings with Israeli officials.
Speaking to reporters on Tuesday, Ms Patel said she did not want to "speculate" on a potential cabinet role, but added it was "important that we have a government that reflects modern Britain".
And former Sports Minister Tracey Crouch, who quit last year in a dispute with the Treasury over fixed-odds betting terminals, could also be in line for a recall.
A source close to Mr Johnson said: "Boris will build a cabinet showcasing all the talents within the party that truly reflect modern Britain."
Meanwhile, Tory donor Sir Mick Davis has resigned as chief executive of the Conservative Party, saying the new leader should be able to choose his own team.
In a letter, he urged fellow donors to get behind Boris Johnson, adding the new PM "can only be effective if a strong and unified party stands behind him".
Mr Johnson will inherit a wafer-thin parliamentary majority and, like his predecessor, will continue to rely on the support of the Democratic Unionists of Northern Ireland to govern.
Labour, the Lib Dems and the SNP have said they will oppose him over Brexit, although they have stopped short of threatening an immediate vote of no confidence.
Shadow international trade secretary Barry Gardiner said "discussions are ongoing" between Labour and potential Tory rebels to find out who might support such a vote.
He told Radio 4's Today programme it was "the nuclear option" which should be "used carefully".
Brexit Party leader Nigel Farage has said he is open to an electoral pact with Mr Johnson - if the new Tory leader is genuine about taking the UK out of the EU on 31 October.
Mr Farage said Mr Johnson would need to call an election if he wanted a no-deal Brexit, in order to "change the arithmetic" in the Commons.
But Health Secretary Matt Hancock, who is part of Mr Johnson's transition team, said the incoming PM didn't want to see an early election.
"There is no way that we are going to have any kind of electoral pact with the Brexit Party and Nigel Farage," he told the Today programme.
US President Donald Trump, speaking to a right-wing youth organisation in Washington DC, said Mr Johnson and Mr Farage would do "tremendous things" together.
Who is Dominic Cummings?
A political strategist and adviser known for his bullish style, Mr Cummings is a long-time Eurosceptic.
In 2004, he led the campaign against a North East regional assembly, and in 2007 went to work for Conservative MP Michael Gove, first in opposition and then while he served as education secretary.
In 2015, Mr Cummings was appointed campaign director of Vote Leave and became a key architect of its messages, including "take back control" and the controversial "£350m-a-week for the NHS" pledge.
Since the referendum, Mr Cummings has often been outspoken on the Brexit process, describing it in 2018 as having been "irretrievably botched" by the May government.
Laura Kuenssberg said some Brexiteers would be pleased with his appointment, seeing it as a strong sign of Mr Johnson's commitment to a 31 October exit. However, she said there was a lot of very angry water under the bridge between him and Tory MPs on the ERG wing because he refused to allow many of them to be involved in Vote Leave.
Earlier this year, Mr Cummings was found in contempt of Parliament for refusing to give evidence to a committee of MPs investigating "fake news". In return, he accused the committee of "spreading errors and lies".
- Watch a special programme on Boris Johnson: The New Prime Minister with Andrew Marr on Wednesday 24 July at 19:30 BST on BBC One, or afterwards on BBC iPlayer.