Taoiseach (prime minister) Leo Varadkar, who supported the reforms, said it looked as if the country was about to "make history".
Official counting of votes will begin at 09:00 local time.
Those taking part in Friday's referendum were asked whether they wanted to repeal or retain a part of the constitution known as the Eighth Amendment, which says an unborn child has the same right to life as a pregnant woman.
Broadcaster RTE's exit poll suggested 69.4% in favour of the Yes side and 30.6% for No. In Dublin, 79% of people voted for repeal, according to the RTE poll.
An exit poll released by The Irish Times points to 68% Yes to 32% for No.
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