The Irish government has announced it will hold a referendum on the issue in 2015.
A spokesman for the government said it would be "actively supporting" the introduction of civil marriage for same sex couples in the referendum.
The move comes 20 years after homosexuality was decriminalised by the state.
Same-sex couples in the Republic of Ireland have been able to enter a civil partnership since January 2011, but not marriage.
To date, more than 1,500 couples have entered into civil partnerships in the state.
Kieran Rose, chairman of the Gay and Lesbian Equality Network (Glen), said the decision to hold a marriage referendum was "another historic step" in the campaign for equality.
The move was also welcomed by the Equality Authority, Marriage Equality and Amnesty International Ireland.
Noeleen Hartigan, programmes director for Amnesty, said: "This is the first step towards true marriage equality in Ireland.
"It is a tremendous achievement by the LGBTI campaigners and rights groups which have struggled so long to achieve recognition for this fundamental human right," she said.
However, the Catholic Bishop of Kildare & Leighlin, Denis Nulty, said the Catholic Church in Ireland would campaign against the introduction of same sex marriage in the referendum.
He said "the Church regards the family based on marriage between a woman and a man as the single most important institution in any society".
"To change the nature of marriage would be to undermine it as the fundamental building block of our society," the bishop added.
The Iona Institute, which describes itself as an organisation that "promotes the place of marriage and religion in society" said bringing in the reform was about redefining marriage.
Spokesman Dr John Murray said: "This debate is really about the value we attach to a child having a mother and a father as distinct from two fathers or two mothers."
The marriage referendum was recommended by the Constitutional Convention, a body set up to examine several issues in Irish politics and society with a view to reforming the law.
Last April, the convention voted overwhelmingly to recommend that the Irish constitution be changed to allow for civil marriage for same-sex couples.
The Republic of Ireland is to hold a public vote on whether same sex couples should be allowed to marry.