The vote set off immediate celebrations in parliament, prompting cheers, applause and even a song.
The result brings an end to more than a decade of robust and often bitter debate on the issue.
"What a day for love, for quality, for respect," said Prime Minister Malcolm Turnbull.
"Australia has done it."
The legislation sailed through parliament without amendments after Australians overwhelmingly supported the reform in a voluntary national poll.
Australia's governor-general is expected to approve the bill in the coming days, marking its official passage into law.
Emotional MPs hugged each other before supporters in the public gallery began singing "I am, you are, we are Australian".
Earlier, many supporters gathered on the lawn outside parliament. They included prominent same-sex marriage advocates, including former Olympic swimmer Ian Thorpe and local comedian Magda Szubanski.
More than 100 MPs had spoken on the legislation after it was tabled in the House of Representatives.
Many senators and MPs related personal stories in explaining why they supported the bill. One MP's speech ended with a marriage proposal - a first for the lower house.
However, other politicians expressed their opposition.
"It is a special relationship between man and a woman for the purposes, if you are so lucky, for bringing children into the world," Deputy Prime Minister Barnaby Joyce said on Thursday.
The bill to amend the Marriage Act was first introduced in the Senate last month, immediately after a national poll showed 61.6% of Australians favoured change.
The bill includes exemptions for registered religious celebrants, who can refuse to marry same-sex couples on the basis of their faith.
Some conservative politicians had sought to extend exemptions to others, such as non-religious celebrants and businesses, but those proposals failed.
More than 12.7 million people - about 79.5% of eligible voters - took part in the national poll, which ran for eight weeks.
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