The news comes as outgoing Taoiseach Enda Kenny delivered a stark warning to the 38-year-old leader in waiting at his final Cabinet meeting.
“There is a huge difference between leading a country and running a department,” he told Mr Varadkar at the Cabinet table.
Following Mr Kenny’s presenting his letter of resignation to President Michael D Higgins at Áras an Uachtaráin last night, attention has already turned to the formation of the new Cabinet, which will be announced later today.
Supporters of Mr Varadkar, who will become Ireland’s youngest Taoiseach ever, have said they expect Frances Fitzgerald to remain as Tánaiste, despite widespread speculation that she would lose that title.
She is, however, expected to move out of the Department of Justice while Mr Coveney looks set to be moved to the Department of Foreign Affairs, which would see Charlie Flanagan moved elsewhere.
It was suggested that Mr Coveney had actively sought the title of Tánaiste but appeared last night to be content to settle to become deputy leader of Fine Gael.
Mr Varadkar is not expected to announce his new Cabinet until late this afternoon and sources close to him have insisted his final line-up is not yet complete.
Also, it is understood that Mr Varadkar has made a promise to all ministers who are not retiring that they will not be sacked.
Mr Varadkar is juggling geographic as well as gender considerations.
His team are also conscious about widening the strength of party figures as much as possible, in preparation for any general election, and of not “Dublinising” the Cabinet, as one figure said.
Sources also expect that Eoghan Murphy, who was campaign director for Mr Varadkar, will be brought to Cabinet but as a super junior minister, potentially for Brexit or EU affairs, rather than as a full Cabinet minister.
Ms Fitzgerald is the name being associated with Social Protection, while Richard Bruton’s name has been linked with the Department of Justice.
Current chief whip Regina Doherty is also expected to be promoted to a full ministry; one of the names linked with her post is Kilkennny TD John Paul Phelan.
With the amalgamation of Public Expenditure and Finance under Paschal Donohoe, a new role of rural or regional affairs is expected to be created for Michael Ring, the Mayo TD who would be seen to represent the West of Ireland.
The Irish Examiner understands that Mr Varadkar is today to say that he will mandate the Government to build “a republic of opportunity”, as he makes his first address as the country’s new leader in the Dail.
Mr Varadkar is said to concentrate on the challenges posed by Brexit and how he as leader intends on combating it but is also to highlight issues in education, employment, people’s personal lives and their rights, according to sources.
Ahead of his resignation speech in the Dáil. Mr Kenny concluded his final Cabinet meeting in Government Buildings.
According to sources, Mr Kenny was said to be businesslike throughout the entire cabinet meeting, but got emotional towards the end when he said a few words.
It is understood at the end of the meeting, Mr Kenny said a few words to those present and he wished those remaining on in Cabinet well.
At the end of the meeting, Mr Kenny shook all the hands of the ministers present as they left the Cabinet room.
In a short statement to the Dáil, Mr Kenny said he did not want today to be about “glorification or flagellation”, as it “has never been about me” but “about the country”.
“I am the first to acknowledge that I didn’t get everything right,” he said.
He said he was always motivated “by what I believed was in the best interests of the Irish people”.