Varadkar, the son of an Indian-born father and Irish mother, became a doctor before first entering Irish parliament at the age of 27. The referendum passed with 61% of the vote, making Ireland the first nation to legalize marriage equality by popular vote.
Irish PM Enda Kenny resigned as head of the governing Fine Gael party, putting Varadkar and Housing Minister Simon Coveney in the leadership race.
Mr Varadkar takes on the leadership of Fine Gael after current Taoiseach Enda Kenny stepped down last month.
66 year old Kenny was the leader of the party for 15.
The Dublin TD is now expected to be appointed Taoiseach if he gains the backing of the Dáil, which sits again on June 13.
Opposition MPs were quick to denounce Varadkar's election, with his constituency rival Ruth Coppinger of the left-wing Solidarity party claiming that his campaign had given people a glimpse of the kind of divisive policies Fine Gael would like to pursue.
"If my election as leader of Fine Gael today has shown anything, it is that prejudice has no hold on this republic", he said to sustained applause and cheering from his centre-right party faithful.
Varadkar was born in Dublin in 1979, the son of an Indian doctor and an Irish nurse.
Varadkar's conservative views are more than likely what got him elected, even though the country is trying to loosen the age-old reins of social Catholic traditions.
'It's not something that defines me.
"I'd be happy for them to remain in their existing positions", he said.
He is 44 and Mr Varadkar is 38, so either of would be Ireland's youngest ever prime minister.
Two other world leaders, former Belgian Prime Minister Elio Di Rupo and former Icelandic Prime Minister Johanna Siguroardottir, had also gone public with their sexuality.