The survey taken at polling stations across the UK suggests the Tories could get 314 MPs when all the results have been counted in Thursday's election.
Labour would get 266, the Lib Dems 14, UKIP none and the SNP 34, the NOP/Ipsos MORI poll for BBC/ITV/Sky suggests.
The first election results are due before midnight with the final result expected by Friday lunchtime.
The exit poll suggests the Conservatives would be 12 short of an overall majority.
It suggests Labour would gain 34 seats, the Conservatives would lose 17 seats, the Lib Dems would gain six and the SNP lose 22 seats.
The Green Party would be unchanged with one seat and Plaid Cymru would still have three MPs, according to the poll.
In total, 30,450 people were interviewed as they exited from 144 polling stations across the UK.
Conservative Defence Secretary Michael Fallon cautioned against reading too much into projections "before we have had a single actual result".
Labour's John McDonnell agreed that it was too early to call the result, but added that if the poll was correct it would "change the nature of politics" in the UK.
BBC Political Editor Laura Kuenssberg said that if the exit poll was proved to be correct Theresa May's "high risk" gamble in calling an election to increase her majority will have failed.
A total of 650 Westminster MPs will be elected, with about 45.8 million people entitled to vote.
Some votes had been cast before Thursday through postal voting, which accounted for 16% of the total electorate at the 2015 general election, when the overall turnout was 66%.