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.
Despite predictions of a close-run result on the divisive issue, the yes vote managed 66.4 per cent of the vote compared to 33.6 per cent voting no - a majority of 706,349.
But DUP MP Ian Paisley said Northern Ireland "should not be bullied into accepting abortion on demand". It's vital that now, the solidarity witnessed on the island of Ireland is also extended to women in the north, by those in England, Scotland and Wales.
The Irish government is planning to bring legislation before the Dáil, providing for abortion on request up to the 12th week of pregnancy, with a three-day "cooling off" period before medication is administered.
Little said the Prime Minister has been "pretty clear we're all pretty uncomfortable the starting point for abortion in this country is a criminal act".
A socially conservative province where the Catholic and Protestant faiths exert strong influence, Northern Ireland allows abortion only when a mother's life is in danger.
Terminations will not be carried out beyond 24 weeks in those circumstances.
There will be provision for conscientious objection among medical practitioners, although doctors will be obliged to transfer care of the pregnant woman to another doctor.
"Thank you so much for making today possible".
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Sir Vince said the United Kingdom government should take advantage of the current lack of a devolved administration in Northern Ireland.
The forthcoming Domestic Abuse Bill promised by ministers could be used as a vehicle for MPs hoping to change the law in Northern Ireland. Final results were due later on Saturday.
More than 66 percent of voters in what has been a traditionally staunchly Catholic country backed repealing the constitutional ban on terminations, triggering scenes of tearful jubilation in Dublin on Saturday after a divisive and often emotional campaign. "However, today we have ensured that it does not have to be lived again".
"Eventually this. will be put to the test here and we will see what happens then", Mr Little said. "The day we took our place among the nations of the world".
Although the referendum was repealed, abortion won't automatically become legal in Ireland.
"It's incredible. For all the years and years and years we've been trying to look after women and not been able to look after women, this means everything", said Mary Higgins, obstetrician and Together For Yes campaigner.
Ireland's foreign minister, Simon Coveney, stressed that the outcome proved this was "not Dublin versus the rest ... not a rural-urban division".
With almost all constituencies reporting results, the Guardian reported that 67 percent had voted to repeal the provision, with only 33 percent voting to preserve it. "The constitution has changed, but the facts have not", it added.
Roscommon-Galway, the only constituency to reject same-sex marriage, voted for change this time by 57 percent.