Sinn Fein, the party historically linked to the Irish Republican Army, bested centrist parties Fianna Fail and Fine Gael.
The 38-year-old son of an Indian immigrant will be the youngest person to hold office.
Leo Varadkar's victory would show another face of the Catholic country.
Ireland is the latest European nation to be swept into turmoil over austerity.
Polls show that Sinn Féin, which hopes to capitalize on several factors toward what would be a historic victory, could wind up as the second-largest party for the first time in the history of the Republic of Ireland.
The two leaders of the new Irish government have landed in America for St.Patrick' Day with a spring in their step and a desire to write a new chapter in the history of Ireland and America.
Ireland's general election on Friday, February 25th may be about to return the kind of verdict that was so unlikely a few days ago that bookmakers were offering 25/1 on it.
"Investors would prefer to have a new government in place because at the moment you don't know what the policies really are