The telegenic Varadkar made all the running in the race to become next party leader, attracting many early public endorsements from high-profile members of his party.
Leo Varadkar, an Indian-origin doctor and Ireland's first openly gay Minister, on Friday won the leadership race for the ruling party to become the country's youngest-ever and first homosexual Prime Minister-in-waiting.
Varadkar on course to become Ireland's youngest ever Taoiseach.
He has come to personify the liberalisation of a country which was once regarded as one of Europe's most socially conservative nations - homosexuality was illegal until 1993. Varadkar was backed by a majority of the Fine Gael's local council members and, crucially, 51 of its 73 parliamentary colleagues, whose votes counted for 65% of the total.
"It's a dramatic generational shift", said Noel Whelan, a political analyst in Dublin. His party hopes that candor will help in the next elections, while opposition parties hope his blunt style will prove a liability to Fine Gael.
It means that 38-year-old Varadkar becomes Ireland's first openly gay Taoiseach, a fact that worldwide media outlets have been focusing on over the past hour.
"It would be a monumental piece of history for the once-staunchly Catholic country", wrote Gay News in the UK.
It's not something that defines me.
Varadkar was born on January 18, 1979, the son of a doctor from Mumbai who married an Irish nurse he had met in Britain.
Varadkar will be confirmed on June 13.
Mr. Kenny took over as leader of the party in 2002 and was first elected Taoiseach in 2011.
He said Simon Coveney had gained his and the party's admiration for his "principled and spirited" campaign and he looked forward to working with him to bring Fine Gael and Ireland forward.
Votes were tallied and the result announced in the Round Room of Dublin's Mansion House.
Adding: 'I'm not a half-Indian politician or a doctor politician or a gay politician for that matter.
In 2015, Varadkar was widely praised for bravery and honesty when he said publicly spoke about his orientation, the first Irish government minister to do so.