The two contenders to succeed Theresa May will appear on a live ITV debate which could help to decide the outcome of the contest.
Mr Johnson will hope to use the occasion to seal his position as the clear frontrunner, with polls giving him an overwhelming lead among party members.
For Mr Hunt, the Foreign Secretary, it potentially offers a final chance to turn around a contest in which he has been the underdog throughout.
There has been frustration in the Hunt camp at the reluctance of his rival to engage in direct debate.
Although both men have taken part in numerous hustings - where they take questions separately from party members - Mr Johnson has agreed to take part in only one previous TV debate, when there were still five contenders left in the race.
It appears to be part of a safety-first strategy by his advisers who fear a gaffe could cost him a race which would otherwise be in the bag, leading to accusations that he has been running scared.
Mr Hunt has been particularly critical of Mr Johnson's unwillingness to subject himself to more detailed scrutiny earlier in the contest.
Ballot papers started going out last week to the party's estimated 180,000 members, and many will already have voted, meaning that the potential for the debate to alter the course of the contest may be limited.
At a hustings organised by The Daily Telegraph on Monday, Mr Johnson issued a fresh warning to Tory MPs seeking to block a no-deal Brexit.
Former attorney general Dominic Grieve has tabled an amendment to the Northern Ireland Bill - intended to keep government in the province running in the absence of the devolved institutions - requiring Parliament to come back to the issue in October.
The move is designed to try to ensure the next prime minister cannot push through a no-deal on October 31, the current EU deadline for agreeing on a deal, simply by suspending - or "proroguing" - Parliament.
Speaker John Bercow is expected to announce on Tuesday whether he has selected the amendment for debate, giving MPs the chance to vote on it.
Mr Johnson, who has said he will take Britain out of the EU by the end of October "do or die", warned such tactics risked playing into the hands of Jeremy Corbyn and Labour.
"If we don't get Brexit over the line then we face a haemorrhage of support," he said, according to the Telegraph.
"The risk they run is we will hand, by sheer incompetence, this government to a hard line Marxist.
"I make that point to Dominic Grieve and others who didn't want to leave the EU. We've been very, very negative. We need to be much more robust and confident."
Mr Hunt said that he believed he would be able to get a new deal with Brussels - but if that proved impossible he would "batten down the hatches" and prepare for no-deal on October 31.
"I strongly believe if we approach this in the right way, there is a deal to be done," he said, according to the Telegraph.
He went on: "In September I take it to the EU. At the end of September, I make a judgment: 'Is there a deal to be done here?'
"If there isn't one, we will batten down the hatches and be ready for October 31."
Mr Johnson also promised to "fix" the pension cap that has resulted in 90% tax rates for some high earners and has led to doctors refusing to work overtime for fear of receiving hefty tax bills.
"This is something I have raised repeatedly, the £1.1 million pension cap, which is affecting doctors and other people.
"It's obviously wrong, it's causing a real problem, I have raised it repeatedly with the Treasury and they keep telling me they've addressed it but the headlines show it has not been addressed, and we will fix it."