The Eighth Amendment, which states that an unborn child has the same right to life as a pregnant woman, now does not allow abortion even in cases of rape, incest, or fetal abnormalities.
Abortion activists who fought for more than three decades to repeal the amendment celebrated the referendum as a step away from the conservative, Catholic values that have heavily influenced Ireland's politics.
Children's Minister Katherine Zappone said she felt emotional and expressed deep gratitude to voters.
"The role of women in society so much within a single life span, people are much more willing to trust women and pregnant people with their own decisions about their own bodies", she said.
Under current law, the practice of abortion in Ireland is illegal, unless the mother's life is deemed to be endangered.
Voters were asked whether they wanted to keep or repeal the Eighth Amendment to Ireland's Constitution, which requires authorities to treat a fetus and its mother as equals under the law. They show overwhelming support to lift a ban on abortion.More news: SpaceX launches for two customers, misses a fairing recovery
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But Irish campaigners against the changing of the constitution have said they will continue to debate the issue, despite what some have called a "sad day" for Ireland. A year later the law was amended to allow abortions in cases when a woman's life is at risk-but didn't allow the procedure in cases of rape or incest or fetal abnormality.
The ban has led to thousands of women travelling each year to neighbouring Britain, where terminations are legal, or increasingly turning to abortion pills sold online.
It indicated that about 72 percent of women voted "yes" along with about 66 percent of men.
"A day when the people said, "This is our time, this is our Ireland".
Younger voters showed more support for overturning the amendment than older voters, according to RTÉ exit poll projections. "There is no prospect of the (abortion rights) legislation not being passed", he said.
If the "yes" forces seeking a constitutional change prevail as the polls suggest, Ireland's parliament will be charged with coming up with new abortion laws.
The historic vote was on whether Irish women would be able to access abortions in the country, and whether the constitution should be changed to reflect this.