The hour-long debate, entitled "Britain's Next Prime Minister: The ITV Debate", will be broadcast on ITV from 8 p.m. The show will be hosted by journalist Julie Etchingham in front of studio audience of 200 people at MediaCityUK, the BBC reported.
One of the two contenders will succeed Theresa May as the new Conservative leader and Prime Minister, with the winner due to be announced on July 23.
Hunt and Johnson have been participating in hustings across the UK but this is the first time they will share a stage.
The two contenders will face questions from members of the public, including Conservative activists, on Brexit and other issues.
The 160,000 or so Conservative members eligible to take part have already begun voting by post, after ballot papers started arriving at people's homes on Friday.
It will be the first time a sitting British Prime Minister has been chosen by party members.
Hunt had been pressing for the TV debate to take place earlier, warning that many people will have made up their minds before seeing the two men cross-questioned on live TV.
Johnson, is regarded as the clear front-runner in the race, having won the support of more than 50 per cent of Conservative MPs in the first phase of the contest, reports the BBC.
Hunt has in recent days won the endorsements of veteran Conservative leaders John Major and Willian Hague.
Both men have said they would prefer to leave the European Union (EU) on October 31 with a negotiated deal but are willing to get out without an agreement if necessary.
They have also made spending promises and offers of tax cuts - which have been criticised by financial experts and Chancellor Philip Hammond.
( With inputs from IANS )