Others sang songs in the sunshine outside the main Dublin results centre as they awaited the official result.
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".
It will be up to parliament to make new laws to govern abortions now that the public has rejected the constitution's Eighth Amendment in a referendum Friday.
People all around the world are celebrating what they consider a reproductive victory. But he said the vote must be respected.
Another said: "I'm so deeply sorry that you had to suffer".
The still-grieving father of Savita Halappanavar, the 31-year-old Indian dentist who died of sepsis in 2012 after being denied an abortion during a miscarriage, has welcomed the result of Ireland's landmark referendum to overturn the abortion ban, saying "we have got justice for Savita". "That would be wrong".
The vote removes a 1983 amendment that required Irish authorities to defend the lives of a woman and a fetus equally on nearly all abortions.
Thousands of Irish women travelled to the United Kingdom every year for abortions, or sourced abortion pills. It would also likely end the need for thousands of Irish women to travel overseas - mostly to neighboring Britain - for abortions they can't get at home.
Katherine Zappone, the Minister for Children and Youth Affairs, said she is confident new abortion legislation can be approved by parliament and put in place before the end of the year.
"A vote for the freedom to choose, a vote for women's rights, a vote for women's control over their bodies, a vote for women's health & safety, a vote towards equality", she proudly said.
In February, Andrew Little asked the Law Commission to look at changing the policy so abortion becomes a health issue, rather than a criminal one.
Northern Ireland has some of the most restrictive abortion laws in Europe with even rape and fatal foetal abnormality not considered legal grounds for a termination.
Counting is under way in the Irish referendum with exit polls suggesting voters backed a law change.
Exit polls released on Saturday showed that it was a landslide victory with 66.4% of voters on the "yes" side in favor of repealing the referendum. The poll had a margin of error of plus or minus 1.6 percent.