The debate will be aired on ITV and it will be the first time the party leaders go head to head in the election campaign.
Labour Party leader Jeremy Corbyn challenged Mr Johnson to a debate earlier in the week, and on Friday said it was "welcome" that he accepted.
"This is a once in a generation election. So it's welcome that Boris Johnson has accepted our challenge of a head to head TV debate. The choice could not be clearer: Boris Johnson's
Conservatives protecting the privileged few or a Labour government on the side of the many," Mr Corbyn tweeted on Friday.
Mr Johnson also took to Twitter to comment on the debate.
"Looking forward to making the positive case to the country that we should #GetBrexitDone & deliver on the people's priorities - #OurNHS, schools, tackling crime & the cost of living," he said.
The Prime Minister was accused of running scarred from TV debates by rival Jeremy Hunt during the race to take over the Tory Party after the departure of Theresa May.
Mr Johnson did take part in two one-on-one debates during the battle for the Tory crown, but not before Mr Hunt and others placed him under great pressure to do so.
ITV Press Centre made the announcement on Twitter on Friday afternoon and said details of further multi-party debates will be released in due course.
SNP Westminster Leader Ian Blackford MP said: "Given that the SNP may well hold the balance of power in the next parliament, ITV’s proposed head to head debate is deeply misleading for audiences.
“If Boris Johnson and Jeremy Corbyn think they are good enough to be Prime Minister, then they should be up to debating the SNP – and broadcasters should not let them hide from that challenge.
“Instead of one head to head debate and then a further one – potentially including a party that has never won a seat at Westminster – there should be a leading debate that includes the SNP."
Lib Dem MP Chuka Umunna tweeted: "Whatever your politics, this is discriminatory, undemocratic and wrong. Not only is it two blokes deciding to have a debate excluding women, we are not a two party country and the sizeable proportion of the public who want to #StopBrexit won’t have a voice in the room."