The Constitutional Convention has recommended that the Constitution should be changed to allow for civil marriage for same-sex couples.
The vote was 79 in favour and 18 against, with the rest expressing no opinion.
The decision was taken by 29 members of the Oireachtas, three members of the Stormont Assembly and 65 citizens selected by a polling company to represent a cross-section of the Republic's electorate broken down by age, gender and region.
The Government has promised to decide on whether to accept the recommendation after an Oireachtas debate on the Convention's reports later this year.
The outcome represents a major boost for the campaign for equality for gay and lesbian couples and children in their households with the rest of the families in the State.
It comes two years after the legalisation of Civil Partnership.
The Convention heard yesterday that legalising same-sex marriage would improve the status of gay and lesbian couples here in over 160 ways.
However, the Catholic Bishops told the Convention that the move would make the roles of mothers and fathers completely irrelevant in the bringing up of children.
Tanáiste Eamon Gilmore welcomed the decision taken by the Convention.
In a statement he said it was not the role of the State to pass judgement on who a person falls in love with, or who they want to spend their life with.
Mr Gilmore added: “I was always confident that when the case was made the people would see the wisdom of the argument”.
Chair of the Fine Gael LBGT Group and Convention member Jerry Buttimer said the debate on the issue of marriage equality over the past two days was exceptional.
He said the Convention’s endorsement sends a “loud signal to the rest of the world about the value the Irish people place on equality, diversity and inclusiveness”.
Dr Richard O'Leary of Changing Attitude Ireland said the vote showed that Irish people wanted to "end the second class citizenship of gay and lesbians".
However, the co-founder of the Church of Ireland group said the existing strong protections in the Constitution for freedom of religion were "entirely adequate" and there was no need to amend them "in the light of the extension of civil marriage to same-sex couples".
The Irish Council for Civil Liberties, Marriage Equality and Gay and Lesbian Equality Network (GLEN) welcomed the decision as "an historic step".
ICCL Director Mark Kelly said the vote result was a landmark moment in the human rights history of Ireland, which sends a clear message to Government to ask the Irish people to remove one "of the last bastions of official discrimination in Ireland"
Marriage Equality director Moninne Griffith called on the Government to implement the recommendation as soon as possible.
A spokesperson for the Catholic Communications office said: "While the result of the Constitutional Convention is disappointing only the people of Ireland can amend the Constitution.
"The Catholic Church will continue to promote and see protection for the uniqueness of marriage between a woman and a man, the nature of which best serves children and our society."