Liam Glynn, BoyleSports spokesperson said "Now that Enda Kenny has finally made a decision to throw in the towel, the race is on to see who will succeed him as leader of Fine Gael".
Kenny's successor as party leader is set to be elected on June 2 and Noonan may still oversee the flotation of Allied Irish Banks, which he said could happen in the coming weeks, another landmark in the banking sector recovery.
Fianna Fail's Michael Martin is the current 1/2 favourite to be Taoiseach after the next general election with Leo Varadkar next at 9/4 and Simon Coveney priced at 6/1.
Irish Prime Minister Enda Kenny speaks to the media at the general election count centre in Castlebar, Ireland February 27, 2016.
His rival Simon Coveney, 44, fits the more traditional profile of a Fine Gael leader and is steeped in politics.
Minister Varadkar says despite his early lead, he hasn't won anything yet - but he has the best intentions for the country.
Mr Kenny delayed the transition to a new leader on a number of occasions this year, asking colleagues for time to visit the United States for the annual St Patrick's Day celebrations and to meet President Donald Trump, continuing the unique tradition Ireland has of access to the White House every March 17.
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Kenny is the longest serving TD in Leinster House he has been a member of Dail Eireann since 1975.
Speaking in Limerick, Minister O'Donovan said Mr Varadkar had the experience and determination to lead Fine Gael and Ireland into the future. I have chose to implement that decision from today.
I will continue to carry out my duties as Minister for Finance until a successor is appointed.
And she said there are few who have given public service to the extent that Enda Kenny has done.
"His leadership of Fine Gael since 2002 has brought us to our most successful period in government as the largest party in Dail Eireann for the last two terms", Heydon said.
Minister Paschal Donohoe has declared his support for Leo Varadkar in the Fine Gael leadership race.
Around 21,000 Fine Gael members will be entitled to vote with TDs and Senators accounting for 65 per cent of the vote, delegates 25 per cent and local councillors the remaining ten per cent share.
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