With just a handful of seats left to declare in the general election, the BBC forecasts a Tory majority of 78.
The prime minister said it would give him a mandate to "get Brexit done" and take the UK out of the EU next month.
Jeremy Corbyn said Labour had a "very disappointing night" and he would not fight a future election.
The BBC forecast suggests the Tories will get 364 MPs, Labour 203, the SNP 48, the Lib Dems 12, Plaid Cymru four, the 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.
Johnson has addressed cheering party workers at Conservative headquarters, telling them there has been a political earthquake, with the Tories winning a "stonking" mandate, from Kensington to Clwyd South.
POWERFUL NEW MANDATE
Speaking earlier at his count in Uxbridge, west London, where he was elected with a slightly higher majority, Mr Johnson said: "It does look as though this One Nation Conservative government has been given a powerful new mandate to get Brexit done."
He added: "Above all I want to thank the people of this country for turning out to vote in a December election that we didn't want to call but which I think has turned out to be a historic election that gives us now, in this new government, the chance to respect the democratic will of the British people to change this country for the better and to unleash the potential of the entire people of this country."
Johnson became prime minister in July without a general election, after the Conservative Party elected him as leader to replace Theresa May.
Speaking at his election count in Islington North, where he was re-elected with a reduced majority, Mr Corbyn said Labour had put forward a "manifesto of hope" but "Brexit has so polarised debate it has overridden so much of normal political debate".
Labour's vote is down around 8% on the 2017 general election, with the Tories up by just over 1% and the smaller parties having a better night.
In other developments:
.Jo Swinson - who only became Lib Dem leader in July and began the election campaign by saying she aimed to be prime minister - lost her Dunbartonshire East seat to the SNP by 149 votes
.Sir Ed Davey and Lib Dem president Sal Brinton are taking over as interim party leaders
.Nigel Dodds, the leader of the Democratic Unionist Party at Westminster, lost his Belfast North seat to Sinn Fein
REMARKABLE RESULTS FOR CONSERVATIVES
The result so far is remarkable for the Conservatives - better than many of them had hoped for.
They have won a majority which will allow Boris Johnson to make sure Brexit happens next month.
There were some astonishing results, with a number of historic Labour heartlands falling to the Conservatives.
Labour, by contrast, could hardly be in a worse position.
Jeremy Corbyn has made it clear he will go before the next election - but he wants to stay for a period of reflection. Many in his party want him to go immediately.
Downing Street said earlier that if Mr Johnson was returned to Downing Street, there would be a minor cabinet reshuffle on Monday.
The Withdrawal Agreement Bill, paving the way for Brexit on 31 January, would have its second Commons reading on Friday, 20 December.
A major reshuffle would take place in February, after the UK has left the EU, No 10 added, with a Budget statement in March.