Kenny says he is resigning as leader of the Fine Gael part.
The contest for the Fine Gael leadership is decided by an electoral college that gives the parliamentary party, made up of TDs, senators and MEPs, 65% of the vote.
TAOISEACH Enda Kenny will retire as Fine Gael leader, with effect from midnight on Wednesday.
Kenny - who had already announced he would not lead Fine Gael into the election - said he would remain prime minister during the contest, due to be concluded on June 2, and during subsequent talks with lawmakers backing the government.
The Taoiseach got a long standing ovation at the meeting of the Fine Gael Parliamentary Party, which was brought forward an hour and began at 4.30pm.
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.
Kenny is due to visit the USA and Belgium early next month in his final trips as Ireland's Taoiseach, or prime minister.
As prime minister, Kenny was widely praised in the European Union for guiding the Irish economy in the wake of the 2008 financial crisis, which hit Ireland's economy hard.
But at a parliamentary election past year, Fine Gael suffered a backlash from voters who felt the recovery was passing them by.
His replacement will lead Ireland during complex divorce negotiations between Britain and the EU.