In addition to his youth and his openly gay profile, Varadkar also would be the first Irish prime minister from an ethnic-minority background.
Leo Varadkar has become Ireland's youngest and first openly gay Prime Minister-elect.
His election marks another chapter in the social change that has swept through the country of 4.6 million people that only decriminalised homosexuality in 1993 but became the first country to adopt gay marriage via a popular vote in 2015.
"Speaking after the final votes were tallied in Dublin, Varadkar said he was delighted, humbled and honoured to win", the newspaper reports.
Kenny has been prime minister of Ireland since 2011 and leader of the ruling Fine Gael party since 2002.
His rival, a 44-year-old father-of-three from Cork, fared better than expected, meaning Mr Varadkar will have to wait to be appointed Ireland's new premier.
Varadkar campaigned on same-sex marriage and liberalising abortion laws, although like the majority of his party colleagues, he is an advocate of tight fiscal restraint.
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According to the Los Angeles Times, Varadkar was selected to replace current Prime Minister Enda Kenny, set to leave office after announcing that she would step down in May.
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.
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. When the tally was done, Varadkar won 60% of the vote.
The Sydney Morning Herald's coverage told readers that Ireland had just elected its first gay prime minister.
Varadkar's sexual orientation, along with his part-Indian parentage, has already been seized upon by global media as a signifier of Ireland's supposed transition from conservative traditionalism to liberal modernity. After that, 10% of the vote is from 235 local representatives, and 25% from the 21,000 registered members of the party.
He was a practising doctor before joining politics and being elected in 2007.
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