The Marriage Bill 2015 has passed all stages in the Seanad and will now be passed to the President to be signed into law.
Minister for Justice Frances Fitzgerald said that soon we will have Christmas weddings of people who thought they would never be allowed to marry.
She said the first same-sex marriages in Ireland will take place from the middle of next month.
She described the day as "joyous" and "truly historic".
She said that the road to marriage equality has been long but it has involved the entire nation.
Ms Fitzgerald said the journey has not ended, and the people’s decision on 22 May was a powerful riposte to the prejudices of the past.
The minister said the decision has sent a message that homophobia is not acceptable.
She said that marriage has been adopted for a new era but it retains its fundamental character.
She said that "on May 22, the green jersey turned rainbow" and the rights of the majority were extended to the minority. She said the decision resonated internationally.
She said we should take a moment today to celebrate the heroism of the LGBT community.
Citing former US president John F Kennedy, she said: "Change is the law of life and those who look only to the past or present are certain to miss the future."
Fianna Fáil Senator Daragh O'Brien congratulated Senator David Norris for his work on campaigning for LGBT rights and he said it was an honour to be in the chamber to share it with him.
Fine Gael Senator Martin Conway said that today was a historic day and a great day to be involved in politics.
Independent Senator Averil Power said it was a huge privilege to work on the campaign. She said she is delighted to be in the Seanad as the bill passes.
Senator Aideen Hayden said that it is five months to the day since the Irish people voted for marriage equality.
She said that the Labour Party has led the way on marriage equality. She said her party is often accused of not delivering on its promises but Eamon Gilmore did deliver in having same-sex marriage in the programme for government.
Mr Norris said: "This is the end of a 46-year long journey. This is the overwhelming decision of the Irish people. The gay community could not have done this on their own."
He asked Senators to applaud the people in the gallery.
The independent Senator said there is no longer gay marriage, just marriage.
He pointed out that there are countries where it is dangerous and fatal to be gay.
Senator Katherine Zappone said: "There is our time to embrace ... our day has come."
Minister for Health Leo Varadkar, and TDs John Lyons, Jerry Buttimer and Helen McEntee were in the public gallery for the conclusion of this afternoon's debate.
Senator Rónán Mullen said he was really taken by what Senator Zappone said about embracing opponents.
He said that it should not have taken a referendum on marriage to signal united horror at homophobia.
He said that it is important to be magnanimous in defeat.
Senator Gerard Craughwell said: "Today Ireland moved forward and became a state for all citizens."
Senator Sean Barrett said that Minister of State with Special Responsibility for the Office of Public Works Simon Harris should be congratulated for opening up Dublin Castle for an immense party on referendum count day.
Labour Senator Marie Maloney said that Senator Norris ploughed a lonely furrow for many a year so she was delighted to see him here to witness the passing of the bill today.
Senator Jim Walsh said that as a democrat he accepts the decision of the people.
Closing the debate Minister Fitzgerald said it was a huge honour for her to bring the legislation to the Dáil today.
The Seanad has adjourned until next week.
