Labour Party candidate Michael D Higgins is set to become the next president of Ireland.
A poet and scholar, Mr Higgins, 71, is a former government minister.
The BBC reports it is thought he has more than 40% of the first-preference vote and is almost certain of victory. He will be Ireland's ninth president.
Turnout is reported to be about 50%, down from around 70% in the general election in February.
There were seven candidates in the election to succeed President Mary McAleese, who has been in office since 1997.
The president is elected for a seven-year term and can be re-elected only once.
Irish opposition leader Micheal Martin of Fianna Fail has already sent his congratulations to Mr Higgins. Fianna Fail did not enter a candidate following the party's heavy defeat in the general election.
Independent candidate Sean Gallagher has conceded defeat to Mr Higgins.
Counting began on Friday morning and the winner is expected to be announced on Saturday afternoon.