Supreme Court judge Frank Clarke has been nominated by the Cabinet as the next chief justice.
Mr Justice Clarke was one of three candidates on a shortlist drawn up for Government to replace Chief Justice Susan Denham.
Although there was a shortlist of three, Mr Justice Clarke's name was the only one brought to Cabinet for consideration.
A statement from the Taoiseach's department said President Michael D Higgins has been "formally advised ... in accordance with constitutional procedure."
Mr Justice Clarke was appointed to the Supreme Court in 2012. Prior to that he had served in the High Court from 2004, primarily working on commercial cases.
Mr Justice Clarke graduated from UCD in 1972 with a degree in Mathematics and Economics before being called to the Bar in 1973.
It is understood that 15 people applied for the post, arising from the upcoming retirement of Chief Justice Denham.
The issue of judicial appointments has been a theme running through the work of this Government.
The Cabinet is also due to fill vacancies in the Special Criminal Court and the District Court.
The text of new anti-corruption legislation also has to be agreed.
The bill, which takes account of the recommendations of the Mahon Tribunal, will strengthen penalties for corruption with a focus on public officials.
The Cabinet was also expected to give the green light to legislation to pave the way for microbreweries to sell their products on site.
Meanwhile, Fianna Fáil has warned Fine Gael that it must soon agree a way to extend mortgage interest relief (MIR) for homeowners at a reduced rate for another three years.
Fianna Fáil said this commitment in the Confidence and Supply agreement that underpins the Government has to be fully honoured in October's Budget.
Discussions have yet to take place between Fianna Fáil and Fine Gael to agree a way of paying the interest relief at a reduced rate for another three years.
Last year alone, just over €184m was paid out in MIR to 419,400 homeowners who bought their property between 2004 and 2012.
No new mortgages taken out since January 2013 have qualified for this scheme.
Fianna Fáil Finance Spokesperson Michael McGrath said that removing the interest relief suddenly would lead to sharp increases in monthly repayments.
"Many of these mortgage holders are carrying very large mortgages and in some cases are still in negative equity," he said.
A Department of Finance document last year warned that extending the relief "may be unpopular with post-2012 purchasers who have not benefitted from MIR, particularly those who have purchased more recently as house prices have risen again".
A Department of Finance spokesperson said the details of the extension will be set out later this year in Budget 2018.