20 May, 2017
The outgoing premier said past year that he would not lead Fine Gael into the next general election, due by 2021 at the latest.
Mr Kenny has been Taoiseach since 2011 and said he expected a new Taoiseach to be in place by June 2nd.
In what is expected to be a two-horse race, nearly 21,000 Fine Gael party members will vote at 26 polling stations from May 29 to June 1, and the parliamentary party, which includes 73 TDs, senators and MEPs, will vote in Dublin on June 2.
"I will continue to carry out my duties as party leader in an acting capacity until my successor is elected", the 66-year-old said.
Michael Noonan has announced his intention to step down as Finance Minister and that he will not be seeking re-election at the next General Election.
So far none of the other local Fine Gael representatives - MEP Mairead McGuinness and councillors John McGahon, Colm Markey, Dolories Minogue and Richie Culhane - have publicly declared who they will be supporting in the leadership battle.
But at a parliamentary election past year, Fine Gael suffered a backlash from voters who felt the recovery was passing them by.
No formal announcement was made despite rumours to the contrary that party strategists were looking at dates in the second and third week of June.
Mr Kenny is this evening (Wednesday) expected to address the leadership question at a parliamentary party meeting at Leinster House.
"I'm really humbled, really grateful for that", he said.
David Cameron took to Twitter to pay tribute, posting: "Enda Kenny TD was a strong leader for Ireland, a great partner for the United Kingdom, and remains a good friend".
Speaking on Newstalk Breakfast earlier, the Public Expenditure Minister described Varadkar as "the most substantial and capable politician of my generation".
She is among four Ministers and four TDs who added their support to Mr Varadkar's campaign to succeed Enda Kenny during the day.
With the current minority government set to run until the end of next year, Fine Gael hope either Social Protection Minister Leo Varadkar, 38, or Housing Minister Simon Coveney, 44, will give them a boost ahead of the next election.