When the Attorney-General ratifies the law, same-sex marriage will finally be legal.
Marriage equality campaigners have fought for years for Thursday's vote.
A short time later, he tweeted: "Out of respect for the millions of Australians who take religious freedom seriously, I moved my amendment, out of respect for the millions who want the SSM bill swiftly passed I chose not to divide on it".
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.
"Love has won, and it's time to pop the bubbly", Greens MP and same-sex marriage supporter Adam Bandt said.
About 12.7 million people participated in the survey, which had a response rate of almost 80% - which is considered very high.
The vote had been called by Turnbull, a moderate who backed gay marriage, in the face of opposition from hardliners who refused to back a national plebiscite on the issue.
"These amendments ensure that people who are legally recognised other than male or female can use the gender neutral term "spouse" to be accurately described in their wedding vows", the memorandum states.
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Lawmaker spent 55 hours across both houses in speeches and debate.
The Bill passed the senate last week, before moving to the lower house on Monday.
Onlookers in the packed public gallery hugged, cheered loudly and started applauding and waving their rainbow flags.
Australia joins about two dozen countries around the world, including Germany, which have legalized same-sex marriage.
But there's another change coming to marriage which means a new word could be popping up a lot more often in the wedding vows, even the straight variety.
Several parliamentarians who supported the changes wore rainbow-coloured socks or ties, including Warren Entsch, described in local media as a "fiercely heterosexual... crocodile-farming, bull-catching Liberal".
"This bill will take from no-one; it simply makes our nation a kinder and a fairer place", Entsch told parliament this week. It was most recently authorised on Tuesday by Austria's top court by 2019 at the latest.