The referendum has exposed bitter divides in Ireland across generational and cultural lines and spurred a debate about national identity.
The pro-choice Yes campaign says repealing the eighth amendment will pave the way for more compassionate laws that will spare women the trauma of having abortions in exile.
But the No campaign says the Government's planned alternative of unrestricted terminations up to 12 weeks will permit "abortion on demand" and put the lives of unborn children at risk in the deeply Catholic country.
In Dublin the pro-choice campaign dominated the streets, which thronged with people wearing "I voted Yes" stickers.
Campaigners in hi-vis jackets brandished placards, while above them, the rooftops were dotted with giant banners.
A handful of pro-life canvassers could be seen making last minute pleas to passers-by. One warned a weary voter that the vote had been hijacked by the "abortion industry".
The Yes campaign has been boosted by large numbers of young voters, many travelling from across the world and posting their stories under the hashtag #hometovote.
For several days at Dublin airport, activists have been gathering in the arrivals lounge, clapping and cheering as they greet Irish expats returning from as far away as Los Angeles, Hanoi and Nairobi.
Meanwhile, Irish Catholic bishops urged voters not to scrap the eighth amendment, as it would be a "manifest injustice" that would "leave unborn children at the mercy of whatever permissive abortion laws might be introduced".
Exit polls point to win for repeal
Official counting began overnight in Ireland's historic abortion rights referendum, and two exit polls predicted an overwhelming victory for those seeking to end the country's strict ban.
The Irish Times and RTE television exit polls suggest the Irish people have voted to repeal a 1983 constitutional amendment that requires authorities to treat a fetus and its mother as equals. Terminations are only allowed when a woman's life is at risk.
The exit polls are predictions only, and official results expected to be announced today.
If the projected numbers hold up, the referendum would be a landmark in Irish women's fight for abortion rights and a key turning point for a largely Catholic nation that has seen a wave of liberalisation in recent years. It would also likely end the need for Irish women to travel abroad - mostly to England - for abortions.
Prime Minister Leo Varadkar, who campaigned for repeal, did not claim victory based on the exit polls but seemed very confident yesterday.
Both exit polls project that the "yes" vote to repeal the ban to be nearly 70 per cent. They also suggest that supporters of more liberal abortion laws may have triumphed throughout the country, not just in the cosmopolitan capital, Dublin, where a strong youth vote had been anticipated.
The magnitude of the predicted victory exceeds the expectations of abortion rights activists, but prominent opponent of repeal Cora Sherlock said the exit polls, if accurate, "paint a very sad state of affairs".
She said the "pro-life movement will rise to any challenge it faces" and resist what she called the trend towards abortion on demand.
If the "yes" forces seeking a constitutional change prevail, Ireland's Parliament will rewrite abortion laws.
The Government proposes to allow abortion in the first 12 weeks of pregnancy and later terminations in some cases.
The large margin of victory predicted by the exit polls would greatly strengthen the Government's hand when dealing with abortion opponents in Parliament.
- additional reporting AP