The RTÉ exit poll also showed an overwhelming majority, 71% have agreed to remove the reference to blasphemy from the Irish Constitution.
While the Irish Times poll conducted by Ipsos/MRBI suggests 69% voted Yes to the referendum.
Michael Nugent from Atheist Ireland says if that is accurate, it will be a great result for freedom of religion, belief, and speech.
"We have to remember that they are only exit polls, they are not official results," said Mr Nugent.
"But even given the largest possible margin of error, it's very positive.
"Whatever the result, we would like to thank everybody who has campaigned for nearly a decade to make this referendum happen and to achieve such a good vote.
"Hopefully, when the full results come in we will have removed a medieval crime from our constitution."
