In the case of a fatal foetal abnormality an abortion can also be carried out.
Support for "Yes" was at 77 percent in Dublin Central, 69 percent in Cork South-Central, 64 percent in Cork North-Central and 60 percent in Galway East.
Chants of "Yes we did" rose from the crowd as the Referendum Commission's Returning Officer Barry Ryan announced the final results.
The referendum saw 706,349 people vote to change the law. A hundred years since women got the right to vote.
"What we've seen is the culmination of a quiet revolution that's been taking place in Ireland over the past 20 years", Prime Minister Leo Varadkar said of the vote. "It's an Ireland that is more tolerant, more inclusive and where he can be whatever he wants without fear of recrimination", said Colm O'Riain, a 44-year-old teacher with his son Ruarai, who was born 14 weeks premature in November.
The outcome was a historic victory for women's' rights in a traditionally Catholic country.
"It's possible even that we could carry every constituency in the country; men and women; nearly every age group and every social class", Varadkar said.
"This is a monumental day for women in Ireland", said Orla O'Connor, co-director of the Together for Yes group.
Northern Ireland's elected assembly has the right to bring its abortion laws in line with the rest of the United Kingdom, but voted against doing so in February 2016 and the assembly has not sat since the devolved government collapsed in January 2017.
Varadkar said he'd like to pass legislation for a new abortion law by the end of the year, according to The Guardian.
Mary Lou McDonald, president of the Sinn Fein party, which campaigned on the yes side, said Ireland has "without doubt done right by Irish women for this generation and many to come". The laws prohibit abortion while the foetus is live, even if there is a threat to the mother's life. The consequent prohibition on abortion was partly lifted in 2013 for cases where the mother's life was in danger.
Supporters of the Yes vote had begun arriving at the castle from the morning as exit polls showed it was a landslide victory for the Yes campaign. Officials results are expected Saturday afternoon.
Anti-abortion activists admitted defeat Saturday, calling the results a "tragedy of historic proportions".
The official vote tally for Friday's vote has not been finished but exit polls predict a massive victory for repealing the constitutional ban. "If and when abortion clinics are opened in Ireland, because of the inability of the Government to keep their promise about a GP led service, we will oppose that as well".
The proposed legislation that will be introduced by the Government will allow abortions within the first 12 weeks of pregnancy.
On Friday, voters in Ireland took to the polling stations to cast their ballots on whether the country should repeal the eighth amendment of its constitution, which effectively bans abortions.
The Irish electorate voted by 1,429,981 votes to 723,632 in favour of abolishing the controversial eighth amendment to the constitution that gave equal legal status to the lives of a foetus and the woman carrying it.
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