Varadkar told the BBC on Saturday that he would campaign for a change in the law, drawing criticism from the former Fianna Fáil minister Willie O'Dea, who said it was "astonishing" that the taoiseach had told "foreign journalists" about his position before the parliament or the Irish people. The Government will aim to hold the vote in late May, but an exact date will not be known until closer the time.
"But I am confident that this timeline can be met. As Minister for Health I became convinced abortion had no place in the Constitution".
"It will be the 36th amendment to our constitution".
Mr O'Donovan said the current state of the law was "not tolerable", but he warned a vote to repeal could have "unintended consequences".
But anti-abortion activists argue Ireland has unique laws which save thousands of lives every year, and that the removal of the eighth amendment would lead Ireland to mimic "ultra liberal" and "abortion on demand" British laws.
Speaking in Dublin tonight, Taoiseach Leo Varadkar said: "We know that thousands of Irish women - from every county in Ireland - go overseas for abortions every year".
Recent opinion surveys suggest there is public support for moderating the laws so that women could have abortions in the first 12 weeks of pregnancy. Incest or rape do not provide legal grounds for abortion in Ireland.
The announcement comes after a special cross-party parliamentary committee said in December that the constitution was not fit for objective and recommended that the eighth amendment should be repealed.
Varadkar, who came to power in June a year ago, pledged to hold the referendum following the non-binding recommendations of a Citizen's Assembly. However, it will only be enacted if the people voted to repeal the Eighth Amendment.
And Labour Party leader Brendan Howlin has welcomed the Government's decision but warned arguments from both sides need to be made respectfully.
The prime minister says his views have "evolved" since he described himself as "pro-life" in 2014.
Terminations are now only allowed in Ireland when the life of the mother is at risk.