Couples and families embraced and cheered when returning officer Riona Ni Fhlanghaile revealed that the vote was carried, 62pc Yes and 38pc No.
Reacting to the results this evening, both the Taoiseach and Tanaiste said Ireland has proven that it is a changed country.
"I know that for tens of thousands of couples and their families, the past 24 hours have been almost like a vigil at the end of a long journey," Mr Kenny said.
"Would their fragile and deeply personal hopes be realised? Would a majority of people in this, our Republic, stand with them and stand up for them so that they can live in our shelter and not in our shadow? That having come out for us, that we could then come out for them, and do it with a solitary syllable, a mark with an 'X'. Today they have their answer."
Mr Kenny appealed to the over one million voters who supported the Yes campaign to continue their participation in future elections.
"For many of you, this was your first engagement in the political process. And I would urge you to continue your participation and your interest because your country needs that participation in our democratic process," Mr Kenny said.
"In the privacy in the ballot box, the people made a public statement. With today's vote, we have disclosed who we are - a generous, compassionate, bold and joyful people," he added.
Meanwhile, Tanaiste Joan Burton said the result is a clear message to emigrants that they can come home and get married in Ireland.
The Labour Party leader said the result is a " magical, moving moment, when the world’s beating heart is in Ireland."
"Not so long ago, to be gay in this country was to risk being criminalised.
And I want to acknowledge those many gay and lesbiancitizens who are still afraid of telling their own story," Ms Burton said.
"Still fearful of the prejudice and abuse, and above all the hurt that might follow.
"I hope that today your fears will begin to fade, and that you can finally feel accepted – and equal – in your own country, as the votes of hundreds of thousands of your fellow citizens have affirmed."