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.
In addition to his youth and his openly gay profile, Varadkar also would be the first Irish prime minister from an ethnic-minority background.
He came out as a gay in 2015 when Ireland became the first country in the world to legalise same-sex marriage through popular vote.
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.
The 66-year old leader was elected Fine Gael's chairman in 2002 and appointed prime minister in 2011.
In the vote, Mr. Coveney secured the backing of a majority of roughly 21,000 grassroots party members, but it was a weighted ballot with the 235 elected councilors and parliamentary party members having the greater say. Now serving as the Minister for Social Protection in Ireland, he is a doctor by profession and started his political career in medical school.
The voting for the Fine Gael leadership is decided in an electoral college system that gives the Fine Gael parliamentary party 65 per cent of the vote.
Varadkar, now one of the youngest Irish PMs, is also first Prime Minister of Asian descent. Even so, opposition parties are not expected to block Varadkar's formal election as prime minister. "It's not something that defines me", he said at the time. He made news in 2015 when he came out as gay, an announcement that was initially met with some shock by his father but who, he said later, was "very supportive".
At 38, Varadkar is now in line to become the youngest person to hold the office of Taoiseach in Ireland.
"I want to thank everyone who engaged in this extraordinary, open democratic process", Varadkar said in his acceptance speech.