The 37-year-old politician is expected to become the youngest prime minister, or taoiseach, in Irish history, The Irish Times newspaper reported on Sunday. Other possible candidates for the party leadership, including Enterprise Minister Simon Coveney and the minister for public expenditure, Paschal Donohoe, stood aside.
Harris was the only candidate to put his name forward to replace Varadkar, and the nomination period closed at lunchtime on Sunday. Harris is expected to be voted in as Ireland's prime minister on April 9 when parliament returns after the Easter break, the newspaper reported.
Varadkar announced his resignation as leader of Ireland and Fine Gael last Wednesday, citing "personal and political" reasons. He pledged to remain in office until his successor was elected.
Harris will take up the post of Prime Minister of the Republic at the age of 37, which will be a record in the political history of Ireland. The previous record was held by the outgoing head of government Leo Varadkar, who managed to take the post at the age of 38.