With ballots in 40 out of 43 constituencies counted, the "Yes" vote was ahead with 62.3 percent, official figures showed, and public broadcaster RTE said the result from the ongoing count was now certain.
Hundreds of "Yes" supporters gathered in the grounds of Dublin Castle cheered and waved rainbow flags as the results came through.
"It's an amazing day to be Irish!" said Rory O'Neill or "Panti Bliss", Ireland's foremost drag queen and a leading "Yes" campaigner, as she arrived at the party wearing a figure-hugging dress and high heels.
"I'm just so happy I could burst. We were voting on whether we were equal in our own country," said O'Grady, wearing a "Yes Equality" T-shirt.
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Legalising gay marriage is a seismic change in Ireland, where the Church remains a powerful force. Homosexuality was illegal until 1993 and divorce until 1996, and abortion is banned except where the mother's life is in danger.
The Archbishop of Dublin Diarmuid Martin, Ireland's top Catholic leader, told RTE that the Church now needed a "reality check".
"It's a social revolution that didn't begin today," said Martin, who had called for a "No" vote arguing that gay rights should be respected "without changing the definition of marriage".