Liberal senator Dean Smith's bill will now become law after a day of cheers, tears and applause in the Lower House.
Turnbull, a gay marriage supporter, says he wants wedding celebrants, not just those affiliated with churches, to have the right to refuse to officiate at same-sex marriages.
The Australian people voted in favour of change by 61.6 per cent, triggering Prime Minister Malcolm Turnbull's promise to change the Marriage Act by Christmas.
The Governor-General now needs to give royal assent to the bill and it will be law, likely within the next few days. "The Parliament has got on with it and we have voted today for a equality, for love, it is time for more marriages, more commitment, more love, more respect, and we respect every Australian who was voted, those who voted yes, and those who voted no, this belongs to us all, this is Australia!"
"We must not fail to recognize that there is honest, heartfelt anxiety about the bill's impact on religious freedom", Turnbull said.
Opposition leader Bill Shorten also spoke ahead of vote, saying: "Australia, we are going to make marriage equality a reality in minutes".
"In my first speech I defined our bond by the ring that sits on both of our left hands, and they are the answer to a question we can not ask", an emotional Wilson said, referring to the first time he addressed the Parliament previous year.
YouTube Canada Reveals the top videos of 2017
It's been produced in Korea, Thailand, Vietnam, and China, but this particular video is from a Thailand show. It was produced by Beth David and Esteban Bravo at the Ringling College of Art and Design.
It follows years of campaigning from the Australian LGBTIQ community and dozens of failed attempts to change the law.
The Senate voted decisively in favour of the legislation last week.
Media captionWill you marry me?
If any of the amendments were successful, the Bill would have to go back to the Senate.
Gay marriage was endorsed by 62 percent of Australian voters who responded to a government-commissioned postal ballot last month.
Australians have always been in favor of same-sex marriage, with polling from as long as 10 years ago showing a majority support for legalizing marriage equality.