Simon Coveney praised his colleague, describing him as an "extraordinary leader" in government
Michael Noonan has announced that he does not want to be considered for Cabinet by the next Fine Gael leader.
Minister Noonan - who has served as Finance Minister since March 2011 - says he believes it is a good time for a new minister to take over the portfolio.
In a statement, he said: "I will not be seeking re-election to Dail Éireann at the next general election. It has been a privilege to represent the people of Limerick since I was first elected in 1981".
He will continue in his ministerial role until a successor is appointed.
Before his current position, Noonan also served stretches as minister for health, justice, energy, and industry and commerce.
He has also been a chairman of the PAC, and was briefly leader of Fine Gael before Enda Kenny took over the role in 2002.
Following Minister Noonan's announcement, a number of politicians praised his time in office.
Speaking as he announced his leadership bid, Housing Minister Simon Coveney said Minister Noonan has been an "extraordinary leader" within government, and a "voice of calm and intelligent commentary".
He added: "I have a message of thanks for him. I think Michael Noonan has played probably the most significant role in rebuilding our economy from the very, very broken state that [he] found it in when he became Minister for Finance."
Fianna Fáil finance spokesperson Michael McGrath said: "There have been many occasions where Minister Noonan and I disagreed on policy, but throughout every one of those disagreements, I have no doubt that he was motivated by a desire to always act in the national interest.
“Despite being a formidable politician and parliamentarian, I developed considerable respect for him, and we, I believe, had a good working relationship."
A number of Labour TDs also paid tribute to their former cabinet colleague, with his fellow Limerick TD Jan O'Sullivan saying: “He has made a substantial contribution to Limerick, and as Minister I found him to be a constructive and supportive colleague in Cabinet."