In a speech outside No.10 following his stunning election victory, the prime minister reached out to Remain backers telling them he would "never ignore" the "positive feelings of warmth and sympathy towards the other nations of Europe".
He added added: "I frankly urge everyone on either side of what are, after three-and-a-half years, a frequently arid argument, I urge everyone to find closure and to let the healing begin."
And he said the main focus of his government - other than getting Britain out of Europe by the end of January - would be the NHS.
Mr Johnson said: "I believe - in fact, I know because I heard it loud and clear from every corner of the country - that the overwhelming priority of the British people now is that we should focus, above all, on the NHS - that beautiful idea that represents the best of our country."
The PM said: "I want everyone to go about their Christmas preparations happy and secure in the knowledge that here, in this people's government the work is now being stepped up.
"To make 2020 a year of prosperity and growth and hope and to deliver a Parliament that works for the people."
He had earlier told supporters that "we smashed the roadblock, we ended the gridlock".
Mr Johnson said: "We did it - we pulled it off, didn't we?
"We broke the gridlock, we ended the deadlock, we smashed the road block."
He went to see the Queen on Friday morning, where he was invited by the Monarch to form a government.
But the "healing" message shared by Mr Johnson did not seem to last long.
On Friday evening police were struggling to contain a protest on Whitehall, which approaches the Downing Street residence of the prime minister.
A gathering of people angry at the decision made by British voters shouted as a line of baton-holding officers attempted to hold them back from approaching the government buildings.
Banner holding protesters shouted: "Boris Johnson, not my prime minister!"
Corbyn to stand down as Labour Party leader
Mr Corbyn - who revealed during a sobering night that he would not continue as leader of the party - has seen just 203 MPs returned, at the latest count.
Mr Corbyn believes the campaign was taken over by Brexit, which cost Labour votes.
Former prime minister David Cameron told ITV News that the result spelled the end of "Corbynomics", which was a good thing.
"First of all, big congratulations to Boris Johnson and all those Conservative candidates who worked so hard. It's an extraordinary result, a powerful result," he said.
"And more to the point it gives us a very strong and decisive government and the opportunity to build the dynamic economy and the good public services that we need in Britain.
"And that's the most important thing of all, winning the trust of people who have put their trust in us, many of them for the first time and Boris has my full support as he does that."
Labour divisions after humbling night
In his first major interview since he saw a humbling night for his candidates, he said he was "very sad" about the result - but warned many areas in the country would continue to suffer under the Conservatives.
The Labour leader said the election was "taken over" by Brexit - and that many had voted for Brexit again through Conservative candidates.
Mr Corbyn said he "everything I possibly could to win this election and to bridge this divide between those who voted Leave and those who voted Remain".
He added: "Of course, I take responsibility for putting the manifesto forward, but I have to say, the manifesto was universally supported, throughout our party and throughout our movement."
Joel Hills explains what the result means for business
While Mr Johnson basked in the election victory, the bitter divisions in Labour quickly emerged.
The results mean the hunt will be on for a new leader - and John McDonnell, shadow chancellor, told ITV News that said he hoped a woman would now take over.
"Brexit dominated the whole debate - we just couldn't get through," he said.
Loyal backers said Mr Corbyn was not to blame for the defeat - but other candidates and party members said it was his name that was being thrown at them on the doorsteps.
Lord Peter Hain, a former Cabinet minister under Tony Blair, said it was an "awful" night.
He said the only surprise was that the Labour leadership was surprised by it.
"It's not good enough that the leadership say it's all about Brexit," he told ITV News on Friday.
"It doesn't mean going for some some wishy-washy, centrist programme, we can have a radical programme but we need a credible leadership."
But, Dan Carden, re-elected for Labour in Liverpool Walton, defended Mr Corbyn, saying he had been "one of the most attacked and smeared leaders of a party we've ever had in this country".
On ITV News' election night special, former Labour home secretary Alan Johnson lambasted Mr Corbyn's leadership.
Sat next to Momentum founder Jon Lansman, Mr Johnson told Presenter Tom Bradby he wants to see the "little cult" sent "out of the party", telling them: "Go back to your student politics."
ITV News Political Correspondent Libby Wiener says Labour's defeat was down to "a disastrous leader and a disastrous campaign".
Misery for Liberal Democrats as Swinson loses
Meanwhile, Jo Swinson's election night turned into a nightmare as she lost her seat to the SNP and saw just 11 MPs returned.
She told supporters on Friday afternoon: "Though I won't be your leader, I will be walking alongside you.
"We will reflect, regroup and refresh.
"We must continue to grow our Liberal movement, both attracting Lib Dem members and by reaching out to work with those who share our values wherever they are."
Former leader, Lord Menzies Campbell, told ITV News that Ms Swinson was not to blame for the humbling night.
He said party members had voted for the controversial revoke position on Brexit but conceded it was "not particularly popular" with the public.
For SNP leader Nicola Sturgeon, however, it was a triumph as she saw a surge in support north of the border.
Her party secured 48 seats - up 13 on the 2017 showing - reinforcing her demands for a second independence referendum in Scotland.
She said: "Westminster has ignored people in Scotland for three years. Last night the people of Scotland said - enough. It is time for Boris Johnson to start listening.
"I accept - regretfully - that he has a mandate for Brexit in England. But he has no mandate whatsoever to take Scotland out of the EU."
However, Brandon Lewis, the Conservative security minister, told ITV News that an indyref2 was not a priority for a Johnson government.
Despite concerns winter weather could put people off heading to the poling booth, voter turnout was only slightly down on 2017.
Some 67.23% of the electorate took part in the snap election, marginally down from 68.7% two years ago.
That contest saw Theresa May lose the slender Tory majority she inherited from predecessor David Cameron.
With every seat declared, some 31,897,334 people took part in the 2019 General Election - thought the Electoral Commission will not be able to verify a figure for a few weeks.
Reaction from overseas
Us President Donald Trump congratulation his "friend" Boris Johnson on a "tremendous victory."
He said Mr Johnson's win would be a "great thing for the United States, also because it means a lot of trade, a tremendous amount of trade."
"They want to do business with us so badly. Under the European Union it was very, very hard for them to do business with us," the President said on Friday afternoon.