With just two seats left to declare, the Conservatives have a majority of 76, reports the BBC.
In a victory speech in London, Johnson said: "We will get Brexit done on time by January 31, no ifs, no buts, not maybe."
He told his supporters "we did it" and it was a "new dawn" for the country - echoing comments former Prime Minister Tony Blair made when he won power in 1997.
He thanked Labour voters, many of whom, he said, had backed the Conservatives for the first time, saying he would lead a "people's government" and fulfil the "sacred trust" placed in him.
"You may intend to return to Labour next time round, and if that is the case, I am humbled that you have put your trust in me, and I will never take your support for granted.
"I will make it my mission to work night and day, flat out to prove that you were right in voting for me this time, and to earn your support in the future," he said.
"And I say to you that in this election your voice has been heard, and about time too. The people want change...we cannot and we must not let them down."
The BBC forecast suggests the Conservatives will get 364 MPs, Labour 203, Scottish National Party (SNP) 48, Liberal Democrats 12, Plaid Cymru four, Greens one, and the Brexit Party none.
That means the Conservatives will have their biggest majority at Westminster since Margaret Thatcher's 1987 election victory.
Labour, which has lost seats across the North, Midlands and Wales in places which backed Brexit in 2016, is facing its worst defeat since 1935; while Jo Swinson has quit as Liberal Democrat leader after losing her seat to the SNP.
The turnout during the election on Thursday hovered at 67 per cent of the 47.59 million registered voters who had been called to the ballot box, 1.6 per cent less than in the 2017 general election.
( With inputs from IANS )