Higgins is followed by independent Sean Gallagher, a businessman and reality TV star, with 30 percent, the BBC reported.
There are seven candidates in the race to succeed President Mary McAleese: Fine Gael's Gay Mitchell, Higgins of the Labor Party, Sinn Fein's Martin McGuinness as well as independents Gallagher, Dana Rosemary Scallon, Mary Davis and David Norris.
Norris already conceded defeat and congratulated Higgins on becoming the next Irish president, the Irish Times reported.
The Labor Party's Joe Costello said while they "can't get a full picture yet," Higgins is doing well in the race with Gallagher and McGuinness, a former IRA commander who is now deputy prime minister in Northern Ireland.
Fine Gael General Secretary Tom Curran said it is a "bad day" for the party, but added, "We accept the result and will move on to work with Michael D to get people back to work."
Voter turnout was estimated at about 50 percent, slightly less than in the parliamentary election this year, The Guardian reported.
The Irish president serves a seven-year term and is limited to two terms in office. The president's role is almost entirely ceremonial and presidents are specifically barred from addressing the nation without approval of the government.
The last two presidents have exercised their right to speak on other occasions, giving frequent interviews.