Those taking part in the 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.
The effective prohibition on abortion in Ireland was partially lifted in 2013 for cases when a mother's life was in danger.
Exit polls indicate Ireland may have voted by a "landslide" to legalize abortion today.
Deputy prime minister of Ireland, Tanaiste Simon Coveney, said in response to the preliminary polling, "Thank you to everybody who voted today - democracy can be so powerful on days like today - looks like a stunning result that will bring about a fundamental change for the better".
Some Irish citizens have framed the debate as "the most contentious social issue that we have had since independence", with pro-choice and anti-choice campaigners-many with ties to the Catholic church, which has a strong influence over the country's citizens-frequently canvassing with pamphlets and marching in the streets over the past nearly three decades.
The count will begin at 9:00am (0800 GMT) on Saturday, with the result expected to be announced at Dublin Castle later in the day. At the Dublin airport, women arrived wearing black shirts emblazonened with REPEAL.
Thousands of Irish women every year cross the channel to have an abortion in the UK.
The referendum vote to repeal the ban in this traditionally Catholic country was predicted to win by a two-thirds majority.
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Activists were out on a final push for votes on Thursday, attempting to convince wavering voters in what has been an emotionally-charged campaign.
Met Eireann predicts a largely sunny day across the whole country, with just a few showers. "Women and girls should not be made into healthcare refugees when they are in a time of crisis", said Niamh Kelly, 27, who paid 800 euros and travelled 20 hours to return home from Hanoi where she works as an English teacher.
While political leaders south of the border were at the forefront of efforts to liberalise the law during the referendum campaign, most politicians in Northern Ireland do not favour a change in the law.
Voting has already taken place on Ireland's offshore islands. Akkamahadevi says that though she was in the hospital, she had checked with her brother to find out if her parents had reached home safely.
After that, abortions will only be allowed until the 24th week of pregnancy if there is a risk to a woman's life, or a risk of serious harm to the physical or mental health of a woman. I wasn't lucky enough to have a daughter.
Letters to the editor published in the Irish Independent newspaper contained several emotional arguments urging voters to reject the repeal movement.
"For Ireland, it's hope for the future", she said of the referendum.
The Taoiseach said the fact that Irish women had to travel to another jurisdiction to end their pregnancies, and sometimes do so in secret, had created a legacy of shame.
Varadkar told reporters that turnout had been good so far and this increased the chances of a vote in favour of liberalising abortion laws.