Same-sex couples who have already wed legally abroad are now automatically recognised in the Irish Republic after the country's marriage equality legislation went into effect on Monday.
Church leaders have labelled the Irish marriage referendum as a "defeat for humanity.''
The law was passed after gaining the people's nod in a national referendum in May, making Ireland the first country in the world to legalise same-sex civil marriage via a popular vote, according to a report by the BBC.
"It's a terrific moment, because our marriage will be the same as any straight couple's marriage from Monday morning," Orla Howard told the BBC in Dublin.
"It will bring all of the rights and protections that marriage brings, from the constitutional point of view, to our family and that's one of the key things for us,'' she added.
Howard married her wife Dr. Grainne Courtney in the United States in May 2013. They have been in a relationship for the last 13 years and live in Dublin with their two grown-up daughters.
The new law also applies to gay couples who want to wed for the first time and those already in a civil partnership in the Republic.
Newlyweds who had already applied to register their civil partnership now have the option to convert this into a marriage application. But those who wish to retain their legal status as civil partners will not be affected by the latest law, according to the BBC.
The Marriage Act 2015 only applies to civil marriage. Irish churches or religious organisations that object to the new law will not be obliged to perform same-sex marriage ceremonies.
During the referendum, Catholic and other Christian organisations campaigned against the legislation, arguing marriage should only be between a man and woman.
Archbishop Eamon Martin told RTE radio One's Sean O'Rourke Show that the Vatican secretary of state, Cardinal Pietro Parolin, was "saddened'' and "felt a sense of bereavement'' when the vote result favoured same-sex marriage.
He said Parolin dubbed the vote result a "defeat for humanity,'' the Irish Times reported.
"One of the difficulties of the debate was that we had two parallel discussions going on. One was about the meaning of marriage and the other was about respecting gay people and showing tolerance,'' he said.
"I think what Cardinal Parolin was expressing was our deeply held conviction about the meaning of marriage. What he was trying to do was express that sense of loss, bereavement even,'' he said.
Martin also said that some people were "disappointed and saddened'' with the result.
Meanwhile, a day after the new law became official, the country's first same-sex marriage ceremony took place in County Tipperary between Cormac Gollogly, a lawyer, and his long-time partner, Richard Dowling, a financier, according to the Telegraph.
The couple, who are both 35 and live in Dublin, have been together for 12 years, the publication said.