The result makes Ireland the first country in the world to do so by popular vote, in a move hailed as a "social revolution".
The first gay marriages are now likely to take place in the early autumn.
Diarmuid Martin, the Archbishop of Dublin, said the Church in Ireland needed to reconnect with young people.
The referendum found 62% were in favour of changing the constitution to allow gay and lesbian couples to marry.
The archbishop told the national broadcaster RTE: "We [the Church] have to stop and have a reality check, not move into denial of the realities.
"We won't begin again with a sense of renewal, with a sense of denial. "I appreciate how gay and lesbian men and women feel on this day. That they feel this is something that is enriching the way they live. I think it is a social revolution."
The Chuch of Ireland has said that while it accepts the State's new legal definition of marriage, the Church defines marriage as between a man and a woman.
"Marriage services taking place in a Church of Ireland church, or conducted by a minister of the Church of Ireland may - in compliance with church teaching, liturgy and canon law - continue to celebrate only marriage between a man and a woman," read a Church of Ireland statement in the wake of the vote.
The Church didn't take a formal position on the issue before Friday's referendum, except other than advising people to "consult their own conscience on the matter."
Out of an electorate of more than 3 million, 1,201,607 backed gay marriage, while 734,300 voters said No. The result prompted a massive street party around the gay district of central Dublin close to the national count centre.
