As opposed to a union between a man and a woman, the same-sex marriage bill recognises marriage as simply "a union between two people".
While marriage equality could become law this week, state marriage registries say they would not have the paperwork to proceed with weddings until January.
"In the course of this week, many hours have been taken up with Labor Party motions about citizenship and penalty rates, matters that could properly have been dealt with after marriage had been dealt with, but no the Labor Party rushed their motion in in the hope that they would get it voted on before the Member for New England made his return".
The historic reforms will commence on Saturday, when same-sex couples can a lodge a notice to marry.
The celebrations started early, with singing and dancing on the lawns of parliament house, where dozens had gathered for a marriage equality rally. In November the results of a forced but not binding postal plebiscite of Australians found over 60 percent support the right of same-sex couples to marry.
"We came, we saw, and love finally conquered", co-chair of the Equality Campaign Alex Greenwich told reporters.
Among them was Christine Forster, the gay sister of Tony Abbott, the former Australian Prime Minister who has always been seen as the face of the "no" campaign.More news: Met office warns of cold weather and possible snow for London
Nearly 80 per cent of eligible voters took part in the poll, and almost 62pc of the 12.7 million people who participated chose "yes" on their ballots.
"And when this law is passed, we should declare that we are no longer a nation of people who voted no". Austria on Tuesday also approved same-sex marriage.
Abbott and other conservatives proposed amendments to the bill to include further religious protections, all of which were voted down. Leading "no" campaigner Lyle Shelton said it was "deeply disappointing" day.
In December 2013, same-sex marriage was very briefly legal in the Australian Capital Territory.
The votes were not counted because the majority wasn't questioned. "And we've seen cheers from the gallery. cheering for the erosion of religious liberty. cheering for the erosion of religious liberty".
An Australian MP named Tim Wilson even proposed to his partner, Ryan Bolger, in the middle of the debates.
The reason being because to do so would, effectively, lead to a legally recognised same-sex marriage. It was most recently authorised on Tuesday by Austria's top court by 2019 at the latest.