Today's vote will test how Ireland weighs women's lives against the rules of the church.
The newspaper exit poll indicated overwhelming support for change.
The now-controversial Eighth Amendment was introduced after a referendum in 1983.
Michelle Sweeney holds a sign to support the reapeal of Ireland's Eighth Amendment.
The poll sampled some 4,000 voters as they were leaving voting stations Friday night.
An earlier Irish Times/IPSOS poll projected a landslide victory with 68 precent voting in favour of the referendum, and 32 percent against it. The RTE poll used similar methods and projected the "yes" vote to be almost 70%. "I hope Ireland will not make the same mistake today". "Whether you agree or disagree, it shouldn't be the government or anyone else making that decision". An Indian dentist, she died in 2012 at 31 in Galway, Ireland, after being denied an abortion while naturally miscarrying.
Vera Rooney voted against repeal.
"Women and girls should not be made into healthcare refugees when they are in a time of crisis", said Niamh Kelly, 27, who paid 800 euros and travelled 20 hours to return home from Hanoi where she works as an English teacher. "I think life is sacred and for that reason I had to vote no".
Since 2013, terminations have only been allowed in Ireland when the life of the mother is at risk, including from suicide.
Those opposed to abortion vowed Saturday to now take their fight to the Irish Parliament, where lawmakers will have to bring about legislation allowing for terminations in the first 12 weeks of pregnancy - and later in cases where there is a risk to the mother's life or the fetus is not expected to survive. After a Supreme Court appeal, she was allowed to travel to the United Kingdom on the grounds that her life was in danger (since she was suicidal as a result of her situation).
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"Yes" campaigners argued that with over 3,000 women traveling to Britain each year for terminations - a right enshrined in a 1992 referendum - and others ordering pills illegally online, abortion is already a reality in Ireland.
RTE's exit poll suggested 69.4 per cent in favour of the Yes side in the referendum and 30.6 per cent for "No".
Thousands of Irish people overseas travelled home to take part in the historic referendum, and supporters of repeal gathered at Dublin Airport to give arrivals an ecstatic welcome.
An Aer Lingus flight attendant pulls her luggage past a new mural of Savita Halappanavar with flowers placed beneath it put up on the day of the Abortion Referendum on liberalizing abortion laws in Dublin May 25, 2018.
"Hopefully it'll be a Yes vote", he said.
Friday's vote came three years after the country legalized gay marriage, which marked another big shift from traditional Irish-Catholic values. A narrow victory might have led to more limited abortion with more stringent conditions attached.
Deputy Prime Minister Simon Coveney said he believed a middle ground of around 40 percent of voters had decided en masse to allow women and doctors rather than lawmakers and lawyers to decide whether a termination was justified.
"If we vote "yes" every unborn, wanted and unwanted, will have zero rights", wrote Frances Kelleher, from Killarney.
She said the "pro-life movement will rise to any challenge it faces" and resist what she called the trend toward abortion on demand.