Until then, women seeking abortions will still have to travel overseas to undergo the procedure.
"The public have spoken".
A vote in favour of repeal paves the way for the Dáil (Irish Parliament) to legislate for change which would see the introduction of a much more liberal regime.
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".
The Eighth Amendment to Ireland's constitution, passed in 1983, gave equal rights to mothers and unborn children.
With polling data suggesting seven out of 10 voters backed reform, campaigners in favour suggested it meant a moment of profound change - when the nation had collectively stood up for women and their healthcare. Current law prohibits all abortions in Ireland, except when the life of the mother is at risk.
Earlier, the No campaigners conceded defeat.
The Save The 8th campaign described the result as a "tragedy of historic proportions". However, a wrong does not become right simply because a majority support it... Voters over the age of 65 were the only ones to come out against the repeal according to projections, with 58.7 percent voting "No".
Official counting for Friday's referendum on whether or not to liberalize Ireland's abortion laws was still underway, and final results were not expected until later Saturday.
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".
"Savita said to her she is not Catholic, she is Hindu, and why impose the law on her".
Children's Minister Katherine Zappone said she felt emotional and expressed deep gratitude to voters.
The first vote I ever cast was in one of the six referendaums that Ireland has had on abortion.
Thousands of Irish citizens living overseas travelled home in droves to exercise their democratic right on the emotive issue.
Savita Halappanavar has been a face of the "yes" campaign, the dentist had sought and been denied an abortion before she died after a miscarriage in a Galway hospital on Ireland's west coast in 2012.
The amendment was introduced after a 1983 referendum that approved a constitutional ban on abortion.
Irish citizens from all over the world flew to Ireland to vote in the referendum, and the hashtag #HomeToVote was trending on Twitter this week.
Varadkar's government has proposed that if the amendment is repealed, abortion will be allowed in the first 12 weeks of pregnancy and between 12 and 24 weeks in exceptional circumstances.