Theresa May says Mr Johnson's immediate priority will be to leave the EU "in a way that works for the whole of the UK".

"To serve as prime minister of the UK is a great honour," she says.

"You achieve nothing alone and so my final words are of sincere thanks to my colleagues."

Theresa May confirms she will advise the queen to invite Boris Johnson to form her government.

She wishes him "good fortune in the years ahead".

Mrs May has emerged out of No 10 to make her final speech as prime minister.

After PMQs earlier, she had lunch in the garden with her husband, Philip.

BBC News Channel

On what awaits Boris Johnson in Northern Ireland, BBC News Ireland correspondent Chris Page said: "This part of the UK certainly will present big challenges for the new prime minister in a number of ways.

"The border backstop is one of the main reasons Theresa May's Brexit deal didn't make it through Parliament.

"The backstop is the insurance policy, the fallback arrangement, that would kick in if there's no free trade deal between the UK and the EU in the future, and would mean there wouldn't be any new checks on that land border but it would mean that the whole of the UK would remain, in effect, following EU customs regulations."

"It's fair to say Boris Johnson is alert to the challenges when it comes to Scotland," says the BBC's Scotland correspondent Lorna Gordon.

"He has already said when he assumes the title of prime minister he will also add alongside that minister for the union."

But she adds: "I really think the response here in Scotland has been fairly muted at best.

"The SNP earlier today saying he has no mandate in Scotland - First Minister Nicola Sturgeon saying she has profound concerns about a Boris Johnson premiership."

But it's not just the SNP who are muted, says our correspondent.

"The two most senior Conservative politicians here have been lukewarm in their support for Boris Johnson thus far."

Scottish Secretary David Mundell said a few months ago he would find it difficult to serve in a Boris Johnson cabinet, although he's changed his position a bit since then - so "it will be interesting to see what happens in the cabinet reshuffle later on".

"And then there's Ruth Davidson, leader of the Scottish Conservatives, she's not a fan either."

BBC News Channel

The BBC's Sian Lloyd in Cardiff says "there is some apprehension" in Wales as to where a Boris Johnson leadership could lead.

The leader of Plaid Cymru in Wales, Adam Price, has already written to Boris Johnson to warn him that "he will be the most irresponsible prime minister in a generation" if he presses ahead with no deal.

Alun Cairns, current Wales Secretary, has made it clear that he is keen to keep his current job.

BBC News Channel

The BBC's Political Editor Laura Kuenssberg says that "we may well see new rebels in the Conservative party".

Who a prime minister picks for their first cabinet "tells us an enormous amount" about their intentions during their time in office.

A lot of Conservative eyebrows "are being raised" by appointing Dominic Cummings to a position within Number 10 - as a senior adviser.

"Big name jobs are going to go to Brexiteers" she says, faces like Dominic Raab and Priti Patel will come back to the frontbenches.

New Lib Dem leader Jo Swinson asked Theresa May what advice she would give to women dealing with men "who think they can do a better job, but are not prepared to do the actual work".

In reply, the outgoing PM urged all women to "be true to themselves" and "persevere", before congratulating Jo Swinson on her appointment.

Mrs May noted how many female party leaders there were in the House, adding that Labour was "the only party letting the side down".

BBC Radio 5 Live

BBC Radio 5 Live's Emma Barnett challenges Conservative minister Nadhim Zahawi over the details of Boris Johnson’s Brexit plan.

The World at One
BBC Radio 4

Image source, UK Parliament

Housing Minister Rishi Sunak says he doesn't know if he will get a job in a Boris Johnson government.

"There will be more women in this cabinet than there have been previously" he states.

The chancellor handed in his letter of resignation following Mrs May's final appearance at Prime Minister's Questions.

Image source, Getty Images

In a pointed message to Mr Johnson, the outgoing chancellor warned that the headroom built up in the public finances could only be used for tax cuts and spending boosts if a Brexit deal was secured.

In his letter to Mrs May, ahead of her own resignation as PM, he said: "We bequeath to our successors genuine choices, once a Brexit deal is done: the ability to choose, within the fiscal rules, between increased public spending, reduced taxes, higher investment or progress towards faster debt reduction - or some combination of all four.

"After a decade when the aftermath of the 2008-09 recession meant we had no choices, this is a luxury which our successors should use wisely."

Philip Hammond has quit as chancellor ahead of Boris Johnson entering Downing Street - just as he promised to do.

Mr Hammond, a staunch opponent of a no-deal Brexit, said the new PM should be "free to choose a chancellor who is fully aligned with his policy position".

In his resignation letter to Theresa May, Mr Hammond said: "Despite the uncertainty created by the unresolved issue of Brexit, we have been able to make notable progress in rebuilding the public finances and preparing the British economy for the opportunities ahead."

BBC Radio 5 Live

The contrast between some Conservative MPs' actions during Mrs May's reign and their words today has not gone unnoticed:

House of Commons
Parliament

Image source, HoC

Mother of the House Harriet Harman says "even her harshest critics" should realise that May has a commitment to public service. But: "Sometimes, you just have to be a bit more careful when a man wants to hold your hand," she says, referring to when Donald Trump held hers.

Mrs May says that having more women in Parliament "has started to change the face of this House". She says it will be her first time in 21 years being a backbencher.

In the last three years she has answered more than 4,500 questions over 140 hours.

"That duty to serve my constituents will remain my greatest motivation," she says, and she teared-up slightly before leaving the chamber.