Dragons’ Den star Gavin Duffy will oversee proceedings and put questions to the two ministers in front of an audience made up of members, councillors, the general public and media.
While the four debates in Dublin, Carlow, Galway and Cork, will not be televised, they will be streamed live on Fine Gael’s Facebook page.
Party members have also been asked if they would like to submit questions for the two contenders to answer and there will also be a question and answer session from the floor after both have debated topics.
Dragons’ Den judge Gavin Duffy explained: “These events are traditional-style political hustings where each candidate is afforded sufficient and equal time to detail their qualifications, experience and ambitions for the party and the country.
“I want to commend Fine Gael for the open and transparent manner in which the election of the leader is being conducted.”
Votes for the contest are weighted in accordance with the Fine Gael electoral college rules, with the 73 members of the Parliamentary Party (PP) accounting for 65%, almost 21,000 party members accounting for 25%, and 235 local representatives (232 councillors and three Údarás na Gaeltachta members) accounting for the remaining 10% of the vote.
Following an introduction by Mr Duffy and the chairman of the hustings, Simon Coveney and Leo Varadkar will deliver a 10-minute opening speech each. They will alternate the order in which they speak over the course of the four hustings.
A question and answer session will then be convened by Mr Duffy after each speech, followed by an open forum to allow for questions from Fine Gael members.
Queries for the four debates can be submitted through Fine Gael and question cards at the venues on the night.
Voting will start at 28 stations around the country on Monday through to Thursday next week before the final parliamentary party vote on Friday when the winner will be declared.