In a statement to colleagues in Dublin, Mr Kenny said he was retiring from midnight with his successor to be in place on June 2.
“I want to assure people that throughout this internal process, I will continue to carry out my duties and responsibilities as Taoiseach in full,” he said.
The veteran politician, from Castlebar, Co Mayo, is to resign after 15 years at the helm of the party and more than six years at the head of government.
Mr Kenny revealed his decision to stand down at a private meeting of the Fine Gael parliamentary party and after delaying the announcement for several months.
Mr Kenny said he would give his successor a “brief but appropriate” time to hold talks with parties and independents propping up the Republic’s minority government.
“I would like to stress the huge honour and privilege that it has been for me to lead our party for the past 15 years, in opposition and into government on two successive occasions,” he said.
“I thank all our members, past and present, for that privilege.”
Mr Kenny paid tribute to loyal constituents and supporters in Mayo who he has represented since 1975 and to his personal staff.
“I especially want to thank my wife Fionnuala, our children, my siblings and their families for their understanding of my work, and indeed for accepting the many intrusions of politics into family life in the interest of building our country.
“I could not have engaged as I did without that base,” he said.