The Taoiseach Leo Varadkar has said it is "an historic day for Ireland", after the majority of voters chose to repeal the Eighth Amendment.
The results seemed to be heading for a Yes vote from early on Saturday, with two separate exit polls on Friday predicting a landmark vote.
In the end, every constituency voted to repeal the amendment - except Donegal.
National turnout was at 64.13% - with 66.40% voting Yes and 33.60% voting No.
Following the result, Mr Varadkar told reporters: "Today is an historic day for Ireland. A quiet revolution has taken place, and a great act of democracy.
"A hundred years since women got the right to vote. Today, we as a people have spoken. And we say that we trust women and we respect women and their decisions.
"For me it is also the day when we said 'No More'.
"No more doctors telling their patients there is nothing that can be done for them in their own country.
"No more lonely journeys across the Irish Sea. No more stigma. The veil of secrecy is lifted. No more isolation. The burden of shame is gone."
Yes campaigners with their posters celebrating their win in Dublin Castle after the the Yes vote won the Irish referendum to repeal the 8th Amendment | Image: Leah Farrell/ RollingNews.ie
He said "almost every county, every constituency, men and women, all social classes, almost all age groups" voted to change the law - contrasting to 1983 when we voted to insert the Eighth Amendment into the Constitution.
"We are not a divided country. The result is resounding."
"This gives us the mandate we need to bring forward legislation and secure its passage by the end of the year."
"Today I believe we have voted for the next generation. We have voted to look reality in the eye and we did not blink.
"We have voted to provide compassion where there was once a cold shoulder, and to offer medical care where once we turned a blind eye."
Speaking directly to those who voted No, Mr Varadkar added: "I know today is not welcome. You may feel that the country has taken the wrong turn, is no longer a country you recognise.
"I would like to reassure you that Ireland is still be the same country today as it was before, just a little more tolerant, open and respectful."
The Taoiseach Leo Varadlkar with Minister for Children Katherine Zappone (left) in Dublin Castle as the results in the referendum to repeal the 8th Amendment were coming through | Image: Leah Farrell/RollingNews.ie
He thanked "all of you who brought us here" - members of the Citizens Assembly, the Oireachtas All-Party Committee and the leaders of the main political parties.
He also thanked "those involved in the civil society campaign who have been working on this issue for many, many years - especially those who opened their hearts and shared their personal stories."
"Above all, I would like to thank the citizens for coming out and voting in such numbers.
"Listening to the arguments on both sides over the past few weeks I was struck by what we had in common, rather than what divided us. "
Mr Varadkar concluded: "Everyone deserves a second chance. This is Ireland’s second chance to treat everyone equally and with compassion and respect."
