As the parliamentary party has a 65% say in the contest, this has provided the Minister for Social Protection with a significant lead over his Cork-based Cabinet colleague. Varadkar will be Ireland's youngest prime minister.
Leo Varadkar will become the Republic of Ireland's next taoiseach, or prime minister, after being named the new leader of the Fine Gael party.
Mr Kenny announced last month he was stepping down after 15 years leading Fine Gael.
Mr Varadkar, who came out as gay in the run up to the 2015 same-sex marriage referendum, has been in charge of the welfare system.
Turning to the runner-up Mr Coveney, he said more united than divided them and "I know we are going to work together to bring Fine Gael and Ireland forward".
Leo is set to become Ireland's new Prime Minister on 13 June. Varadkar will be the country's first gay leader. As head of the ruling party, he will become prime minister.
During the campaign, Varadkar's political opponents claimed he would pull Ireland too much to the right.
Varadkar, son of immigrant Indian doctor Ashok Varadkar and Irish nurse Miriam and himself a doctor, was born and raised in Dublin and worked as a general practitioner before winning a seat in the Parliament in 2007. Prior to becoming a politician, Varadkar was a doctor; his partner, Matthew Barrett, is also a doctor.
"It is just part of who I am", he said at the time.
"It is not something that defines me".
Varadkar would be one of two openly gay heads of state now in office - Luxembourg's prime minister Xavier Bettel being the other.
Varadkar might seem to be an unexpected pick for leader of Ireland - a country that's still finding its secular European footing after years of church influence over the state.