The Prime Minister said he was "humbled" by the support of former opposition party backers as he delivered his victory speech in central London this morning.
Mr Johnson addressed those who may never have voted Tory in the past and only "lent" their vote this time.
"Your hand may have quivered over the ballot paper before you put your cross in the Conservative box and you may intend to return to Labour next time round," he said.
Conservative victories in a string of seats in Labour’s former heartlands meant that the party secured its biggest majority in the House Commons since Margaret Thatcher in 1987.
Speaking this morning, Mr Johnson promised to “get Brexit done by January 31, no ifs, no buts, no maybes.”
He said he was humbled by all those who switched their vote to the Tories, vowing “we will never take your support for granted”.
Mr Johnson called Brexit the “irrefutable, inarguable” decision of the British people and said the threat of a second referendum had ended.
Addressing his own party he said: “We did it – we pulled it off, didn’t we?
“We broke the gridlock, we ended the deadlock, we smashed the road block.
“I want to congratulate absolutely everybody involved in securing the biggest Conservative majority since the 1980s.
“Literally – as I look around – literally before many of you were born.”
The PM pledged to "put an end" to the "squabbles and all that nonsense," confessing: "Because we politicians have squandered the last three years, three and a half years in squabbles.
"We’ve even been arguing about arguing, and arguing about the tone of our arguments," he added.
He then reiterated his promise to deliver 50,000 more nurses, 50 million more GP surgery appointments, 20,000 more police officers and 40 new hospitals, and stressed the Government would ensure the UK's carbon neutrality by 2050.
The Tory leader then committed to an overhaul of Parliament, saying MPs must work for all British people.
“In winning this election we have won votes and the trust of people who have never voted Conservative before and people have always voted for other parties," he said.
"Those people want change. We cannot, must not, must not, let them down."
The PM's de facto chief of staff and notorious advisor Dominic Cummings claimed no credit for the Tories' landslide win.
He said: “After the shock of the referendum, MPs and journalists should have taken a deep breath and had a lot of self-reflection of why they misunderstood what was going on in the country but instead a lot of people just doubled down on their own ideas and f****d it up even more.
“That’s why something like this happens against expectations.
“All these better-than-average educated Remainer campaigner types who have waved around for eight weeks, for the last four months and didn’t understand what was going on and didn’t understand they were driving everyone mad," he added.
It comes after Mr Johnson delivered a private speech to Conservative aides this morning, claiming the party now had a "stonking mandate" to deliver Brexit.
The Prime Minister credited his Tories with creating earthquake, saying: "We must understand now what an earthquake we have created. The way in which we have changed the political map in this country," BuzzFeed News reported him as saying.
"We have to grapple with the consequences of that. We have to change our own party. We have to rise to the level of events.
"We have to rise to the challenge that the British people have given us.”