Boris Johnson has become Prime Minister after a meeting with the Queen in Buckingham Palace.
The Tory leader, whose progress to his meeting with the Queen was briefly disrupted by climate change protesters, was appointed after Theresa May resigned.
The new Prime Minister has made clear he will leave the European Union on October 31, with or without a deal, but Mrs May used her farewell statement to say his priority must be a Brexit "that works for the whole United Kingdom".
Minutes after Mrs May left Buckingham Palace to offer her resignation to the Queen, Mr Johnson arrived to be appointed as her successor.
As his car drove along The Mall to the palace, banner-waving climate change protesters from Greenpeace attempted to impede its journey.
Mrs May's farewell speech in Downing Street was also disrupted, by a cry of "stop Brexit" from a protester outside, in reply she joked: "I think not."
But she made clear her desire for Mr Johnson to seek a deal with Brexit, having previously warned about the risks of a no-deal departure.
Flanked by husband Philip, she said: "I repeat my warm congratulations to Boris on winning the Conservative leadership election.
"I wish him and the Government he will lead every good fortune in the months and years ahead.
"Their successes will be our country's successes, and I hope that they will be many."
But she added: "Of course, much remains to be done – the immediate priority being to complete our exit from the European Union in a way that works for the whole United Kingdom.
"With success in that task can come a new beginning for our country – a national renewal that can move us beyond the current impasse into the bright future the British people deserve."
One of Mrs May's final acts as prime minister was to receive the resignations of Philip Hammond, David Gauke and Rory Stewart from their Cabinet roles.
Her effective deputy prime minister David Lidington also announced he was standing down from the Government.
Mr Hammond, Mr Gauke and Mr Stewart strongly oppose a no-deal Brexit and say they cannot support Mr Johnson's commitment to take Britain out of the EU by the deadline of October 31 "do or die".
In his resignation letter, Mr Hammond said the new PM should be "free to choose a chancellor who is fully aligned with his policy position".
And in a pointed message to Mr Johnson, he warned that headroom built up in the public finances could only be used for tax cuts and spending boosts if a Brexit deal was secured.
Mr Gauke used his resignation letter to say: "Given Boris's stated policy of leaving the EU by October 31 at all costs, I am not willing to serve in his Government.
"I believe I can most effectively make the case against a no-deal Brexit from the backbenches."
Mr Lidington stood down as Mrs May resigned and said he had informed Mr Johnson of his decision, saying it was "the right moment to move on" after 20 years on the frontbench in government and opposition.
He said he would do all he could to help the new government "secure a deal to allow an orderly departure from the EU".
Mr Johnson has been busy in his preparations for government, with a return expected for Eurosceptic Priti Patel and an advisory role for Leave campaign mastermind Dominic Cummings.
Ms Patel is an ardent Brexiteer who was forced by Mrs May to resign as international development secretary over unauthorised contacts with Israeli officials.
Mr Cummings clashed with officials and politicians while he was an adviser to Michael Gove in the coalition government, but Mr Johnson clearly believes his forthright style will help steer Brexit through.
The appointment of the abrasive Vote Leave campaign director will be controversial given that earlier this year he was found to be in contempt of Parliament for refusing to give evidence to a committee of MPs investigating "fake news".
He is also less than impressed with the calibre of Brexiteer MPs, describing a "narcissist-delusional subset" of the European Research Group (ERG) as a "metastasising tumour" that needed to be "excised".
Mr Johnson will need the support of those same ERG hardliners for his Brexit plan.
Ms Patel has reportedly been lined up for the post of home secretary as allies said Mr Johnson was determined to create a "Cabinet for modern Britain", with a record number of ethnic minority ministers and more women attending in their own right.
It is likely to mean a promotion for the Indian-born employment minister Alok Sharma, who is expected to take his place around the top table.
But uncertainty surrounds the future of Mr Johnson's defeated leadership rival Jeremy Hunt after he reportedly turned down a demotion from Foreign Secretary to defence secretary.
In her final session of Prime Minister's Questions, Mrs May used an ill-tempered set of exchanges with Labour leader Jeremy Corbyn to call for him to also quit his post.
After Mr Corbyn accused her of a string of policy failures and U-turns, Mrs May told the Opposition leader: "Perhaps I could just finish my exchange with him by saying this: As a party leader who has accepted when her time was up, perhaps the time is now for him to do the same?"