The Republic has voted to repeal the eighth amendment of the state's constitution, which prohibits terminations unless a mother's life is in danger.
The historic result put the Yes vote at 66.4% with 33.6% voting No.
Pro-choice campaigners have hailed the Yes vote as a resounding roar for "dignity and decency". Anti-abortion campaigners described the decision as a "tragedy of historic proportions".
Thousands of campaigners gathered at Dublin Castle to hear the result announced at 6.15pm.
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.
Only one constituency voted to retain the eighth amendment. 51.8% of voters in Donegal voted No.
Ireland’s Health Minister @SimonHarrisTD leads the crowds at Dublin Castle in a rendition of the chant “Yes we did”. #8thRef pic.twitter.com/rlqUPtonwd
— David Young (@DavidYoungPA) May 26, 2018
Together for Yes co-director Orla O'Connor paid tribute to the women and couples "whose own bravery and dignity have moved hearts and changed minds - and given the scale of the victory, changed the country".
They sing: “Finally the tables have started to turn...” pic.twitter.com/70tLf8CtCZ
— David Young (@DavidYoungPA) May 26, 2018
The Save the 8th campaign, which conceded defeat on Saturday morning, said a wrong did not become a right simply because the majority supported it.
Communications director John McGuirk said the unborn child no longer had a right to life recognised by the Irish state.
Anti-abortion activist Cora Sherlock tweeted on Saturday evening that it was "a sad day for Ireland and for people who believe in genuine human rights".
Read more: Abortion referendum result 'tragedy of historic proportions'
Today is a sad day for Ireland and for people who believe in genuine human rights. The struggle to defend the most vulnerable has not ended today, it's just changed. Thank you to all the incredible people who worked so hard to protect women and save babies. We fight on. #8thref
— Cora Sherlock (@CoraSherlock) May 26, 2018
Taoiseach Leo Varadkar said the referendum result marked "the day Ireland stepped out from under the last of our shadows and into the light".
It was "the day we came of age as a country" and "the day we took our place among the nations of the world".
"Today, we have a modern constitution for a modern people," he said.
Referencing the poet Maya Angelou's words that history "cannot be unlived" but "if faced with courage, need not be lived again", Mr Varadkar said: "The wrenching pain of decades of mistreatment of Irish women cannot be unlived.
"However, today we have ensured that it does not have to be lived again."
Read more: Pressure mounts for law change in Northern Ireland
Tanaiste Simon Coveney described it as a vote to put a "more compassionate and appropriate" policy in place, one that helped and respected women in vulnerable circumstances.
"This is a huge step forward for Ireland," Mr Coveney said.
Health minister Simon Harris said he could not have predicted the scale of the victory.
"Under the Eighth Amendment, the only thing we could say to women was take a flight or take a boat and now the country is saying no, take our hand, we want to support you," Mr Harris said.
"Women in crisis pregnancy, we were telling them or letting them feel like they were on their own - and today the country is saying no, we want to stand with you."
At Dublin Castle, Sinn Fein president Mary Lou McDonald and deputy leader Michelle O'Neill held up a banner with the words: "The North is next."
Amnesty Ireland executive director Colm O'Gorman said the outcome would be a huge milestone for women's rights.
Children's Minister Katherine Zappone said she felt emotional and expressed deep gratitude to voters.
She pledged the legislation would be introduced quickly, before the end of the year.
Opposition TD Micheal Martin told RTE News that the Irish people had made the right decision and it would mean better care for women in Irish hospitals.
"It's the dawn of a new era," the Fianna Fail leader said.
He said he wrestled with the topic, but that women who told their stories had a big impact on him, especially those who had suffered rape, incest and fatal foetal abnormalities.
The final results of the Referendum on the 36th Amendment of the Constitution Bill 2018:
Yes: 66.40%, No: 33.60%.
Turnout: 64.13%
Electorate: 3,367,556
Total poll: 2,159,655
Invalid ballot papers: 6,042
Valid poll: 2,153,613
Votes in favour: 1,429,981
Votes against: 723,632
