Taoiseach Leo Varadkar has hailed Ireland's blasphemy referendum as a small step towards creating a 21st century constitution.
Commenting on Peter Casey's strong showing in the tally figures, he added: "His profile took off under controversial circumstances, it is a big vote and he has taken votes from would be Fianna Fáil and Sinn Féin voters based on data I have heard elsewhere today".
In his acceptance speech, Mr Higgins said Ireland is at a time of transformation and the momentum of empathy, compassion, inclusion and solidarity must be recognised and celebrated.
According to the Irish constitution, Ireland's president is the head of state, but his job is largely ceremonial in the parliamentary democracy, now led by Prime Minister Leo Varadkar.
Donegal Deputy Pearse Doherty was Liadh Ni Riada's director of elections and both will surely be disappointing that the MEP only managed 4,524 votes in Donegal.
An official declaration will be made in Dublin Castle - but the new presidential term doesn't actually begin until November 11.
"You can't be a racist if you don't regard the people you are talking to as a different race", he said.
If the exit polls are correct, Mr Higgins is likely to be easily re-elected on the first count for a second seven-year term.More news: Angela Merkel 'to abandon key CDU party role'
Many saw that poll as an indication of the Catholic church's declining hold on Irish culture.
Media coverage had focused on the surge in support for independent businessman Peter Casey, who came second with 23 percent of the vote, up from 2 percent in an opinion poll just days earlier.
More than 3.2 million people were entitled to vote in 40 constituencies across the country.
The exit polls suggest the referendum will be passed by a significant majority.
After an at times bruising campaign, the five defeated candidates were united in congratulating returning president Michael D Higgins. Past presidents, even if career politicians, tend to be apolitical once in office. Four presidents - Sean T O'Kelly, Eamon de Valera, Patrick Hillery and Mary McAleese - served for 14 years.
Meanwhile, in rural Limerick, the result of the first count is expected to be announced here at the Limerick Racecourse in the next hour.
The functions of the President of Ireland is limited mainly to representative.