Elections official Barry Ryan said more than 1.4 million voters, or 66 percent of those who cast valid ballots, favored repealing the Eighth Amendment of the Irish Constitution while roughly 724,000 wanted to keep the abortion ban in place.
Irish Catholics attending Sunday Mass were disappointed with the result of a referendum in which voters opted to legalise abortion and think it reflects the weakening of the church - a situation that was unthinkable in Ireland a generation ago.
Until now, women in Ireland seeking abortion have had to travel overseas to England, Scotland or Wales, where termination has been a legal right since the Abortion Act was passed in 1967.
Mrs Halappanavar's death caused worldwide controversy and sparked a campaign to have Ireland's abortion law liberalised.
Lawmakers will now move to allow women to get abortions in the first 20 weeks of pregnancy.
"Remarkable day", Irish Prime Minister Leo Varadkar wrote Saturday on Twitter.
Varadkar said he wanted the law in force by the end of the year and Health Minister Simon Harris told AFP that the cabinet would meet on Tuesday to approve the drafting of legislation.More news: Rafa Nadal storms past Denis Shapovalov into the quarter-finals
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He said the result means that "we are living in a new time and a changed culture for Ireland". The referendum states that abortions should only be performed when the mother's life is in immediate danger, as fetuses have an "equal" right to life.
Mr Little said while Ireland's circumstances were quite different - the result of its referendum did indicate attitudes and values towards abortion were changing.
Former One Direction member and Irish native Niall Horan also shared his thoughts on the vote.
"I feel enormous relief and great pride in the people of Ireland who didn't maybe know what they thought until they were finally asked the questions", Ailbhe Smyth, a women's rights activist, was quoted as telling CNN.
"You can still passionately believe that the decision of the people is wrong, as I happen to do, and accept it", he said. The doctors concluded that a miscarriage was unavoidable but refused to intervene despite requests from Halappanavar and her husband for an abortion as the country's law did not allow it. Halappanavar's condition deteriorated and she was diagnosed with an infection and subsequent septic shock.
"The public have spoken, the result appears to be resounding in favour of repealing the Eighth Amendment, possibly to carry every constituency in the country", Varadkar said on Saturday.
However, Downing Street has rejected the move on the grounds that abortion is a devolved matter that should be decided by the Northern Ireland executive and assembly, both of which have been suspended for nearly 18 months.