The exit poll suggests Johnson's strategy had breached Labour's so-called "Red Wall" of seats across the Brexit-supporting areas of the Midlands and northern England where he cast his political foes as the out-of-touch enemies of Brexit.
US President Donald Trump was quick to congratulate Johnson.
Many Labour figures are calling on Corbyn to resign.
The prime minister issued a direct appeal to potential Brexit Party voters, saying that they were risking the "terrifying prospect of Jeremy Corbyn moving into Downing Street".
"Corbyn was a disaster on the doorstep. everyone knew he couldn't lead the working class out of a paper bag", said Alan Johnson, who served as a senior minister under Blair.
That outcome would allow Johnson to fulfill his plan to take the United Kingdom out of the European Union next month.More news: UK Liberal Democrat leader Swinson loses seat to Scottish National Party
A landslide Conservative win would mark the ultimate failure of opponents of Brexit who plotted to thwart a 2016 referendum vote through legislative combat in parliament and prompted some of the biggest protests in recent British history.
All 650 seats in the House of Commons are up for grabs in the election, which is being held more than two years ahead of schedule.
Frustrated by the country's failure to quit the European Union and at Labour's equivocal stance on Brexit, large numbers of voters deserted the party and flocked to the Conservatives. It's possible he could form a coalition with a smaller party that might give him the votes needed to pass his Brexit divorce bill. Labour Leader Jeremy Corbyn was all smiles after lodging his vote at his local polling station in Islington, London.
Labour, if it is defeated by the margins shown in the exit poll, now faces a civil war between the socialists who control it and more moderate factions which will demand power.
"Boris Johnson has to respect that the Scottish government in Edinburgh already has a mandate for a referendum on Scottish independence in a change of circumstances", said SNP Westminster leader Ian Blackford. In 2017 it correctly predicted a hung Parliament, with no overall victor, and in 2015 it predicted the Conservatives would be the largest party.
Labour, which is largely but ambiguously pro-EU, faced competition for anti-Brexit voters from the centrist Liberal Democrats, Scottish and Welsh nationalist parties, and the Greens.More news: UK Conservative Party projected to win majority
But Labour primarily campaigned on a promise to end austerity by increasing spending on public services and the National Health Service.
It appears that wasn't enough to boost Labour's fortunes. The 70-year-old left-winger was also accused of allowing anti-Semitism to spread within the party.
Corbyn is proposing to renegotiate softer exit terms with Brussels within three months and put them to a new referendum, alongside an option to remain in the 27-member bloc, after a three-month campaign.
"We need to reflect on that and learn the lessons from that".
For many voters, the election offered an unpalatable choice.
Yet, his energy and determination proved persuasive to many voters.More news: Cristiano Ronaldo flips out at pitch invader after Juventus Champions League win
The exit poll, a survey of thousands of people after they voted, has now been released following the close of polls. "With any luck, tomorrow we'll be getting to work".