Only four MPs in the lower house voted against a private bill on Thursday, just over a week after it was agreed to by the Senate.

It went through unchanged, despite a push from conservative politicians for additional exemptions – including for religious organisations, civil celebrants and Defence chaplains.

Prime Minister Malcolm Turnbull told parliament, just after a round of applause across the chamber and in the public gallery, the legal change belonged to all Australians.

“What a day! What a day for love, for equality, for respect. Australia has done it,” he said.

“It’s time for more marriages, more commitment, more love, more respect.”

Labor leader Bill Shorten said the new law spoke for a modern Australia, “inclusive and fair”.

“When this law is passed, we should declare we are no longer a nation of people who voted no, or people who voted yes – we are simply Australians one and all,” he said.

Public gallery erupts into chorus of ‘I Am Australian’ after Parliament votes to legalise same-sex marriage #auspol #SSM pic.twitter.com/uuoePCJamD

— ABC News (@abcnews) December 7, 2017

I’m so proud of these guys today! Proud to be a #RainbowRebel pic.twitter.com/QUKAHulqc1

— Tim Wilson MP (@timwilsoncomau) December 7, 2017

Greens leader Richard Di Natale, who was wearing striped rainbow shoes, said it was a great moment.

“What has been a bleak year for Australian politics, we saw a rainbow poking through,” he told AAP.

Under the new laws, ministers of religion and religious marriage celebrants will be able to act in accordance with their religious beliefs about marriage.

Religious bodies will be able to act in accordance with their doctrines, tenets and beliefs in providing facilities goods and services in connection with marriage.

Both major parties had given their members a free vote on the issue.

More than 120 MPs spoke on the bill, which was sponsored by gay Liberal senator Dean Smith and backed by colleagues Warren Entsch, Trent Zimmerman, Tim Wilson and Trevor Evans.

Former prime minister Tony Abbott, Treasurer Scott Morrison, junior ministers Michael Sukkar and Alex Hawke, and backbenchers Andrew Hastie, Andrew Broad and Sarah Henderson, were unsuccessful in trying to change the bill, as was Greens MP Adam Bandt.

The four MPs who voted against the bill were Liberal Nationals Keith Pitt and David Littleproud, Liberal Russell Broadbent and independent Bob Katter.

The legislation will become law as soon as it is granted royal assent by the governor-general.

Long-time campaigner Shelley Argent, the national spokeswoman for Parents and Friends of Lesbians and Gays, said she lobbied for the bill because of her love for her gay son, James.

“I don’t care if he ever gets married – I just wanted him to have the right,” she said.

Olympian Ian Thorpe said it was incredible to see the parliament in action.

“We just made the country a fairer, more equitable and just place,” he said.

– AAP