But same-sex weddings will not happen in Australia until January 2018 because same-sex couples will still need to lodge a Notice of Intended Marriage, which must be completed a month before the wedding.
After the bill passed the Senate last week, House proceedings kicked off with fireworks Monday when Liberal MP Tim Wilson surprised his colleagues by proposing to his long-time partner Ryan Bolger.
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.
Prime Minister Malcolm Turnbull looked particularly pleased, though he was criticised on Twitter, and accused of trying to take credit for this.
"We must not fail to recognize that there is honest, heartfelt anxiety about the bill's impact on religious freedom", Turnbull said.
The votes in favour of the bill were not even counted as a majority was not questioned.
"There's only one thing left to do: Ryan Patrick Bolger, will you marry me?" "Equality isn't in our legal birthright of every Australian and this equality is long overdue", said Mr Shorten.
If any of the amendments were successful, the Bill would have to go back to the Senate. Though the bill was expected to pass into law without significant opposition, the lengthy legislative process was excruciatingly slow for the hundreds of advocates watching from the public gallery. Gay marriage was endorsed by 62 percent of Australian voters who responded to a government-commissioned postal ballot by last month.
The only potential obstacle to the law passing on Thursday would be if marriage equality opponents managed to amend the legislation.
Liberal MPs Jason Falinski and Trent Zimmerman gave their support to the bill.
The House of Representatives is holding its final two-week session of the year, which is giving priority to lifting the ban on same-sex marriage in Australia.