The non-binding postal vote showed 61.6% of people favour allowing same-sex couples to wed, the Australian Bureau of Statistics said.
Jubilant supporters have been celebrating in public spaces, waving rainbow flags and singing and dancing.
The issue only went to a voluntary postal vote after a long and bitter debate about changing the law.
Prime Minister Malcolm Turnbull said his government would now aim to change the law in parliament by Christmas.
“[Australians] have spoken in their millions and they have voted overwhelmingly yes for marriage equality,” Mr Turnbull said after the result was announced.
“They voted yes for fairness, yes for commitment, yes for love. And now it is up to us here in the parliament of Australia to get on with it.”
More than 12.7 million people – about 79.5% of eligible voters – took part in the eight-week postal survey
The result on Wednesday brings an end to what was at times a heated campaign. The vote itself had been criticised by same-sex marriage supporters, many of whom said it was unnecessary when parliament could debate the issue directly.
The survey was voluntary, unlike Australia’s compulsory elections.
Voters were asked to mail back a Yes or No response to the question: “Should the marriage law should be changed to allow same-sex couples to marry?”
The Yes campaign argued that it was a debate about equality. The No campaign had put the focus on the definition of family, raising concerns about how issues like gender will be taught in schools.
Australia’s chief statistician David Kalisch said about 7.8 million people voted in support of same-sex marriage, with approximately 4.9 million against it.
He said participation was higher than 70% in 146 of Australia’s 150 electorates. All but 17 electorates supported changing the law.
“This is outstanding for a voluntary survey and well above other voluntary surveys conducted around the world,” he said.
“It shows how important this issue is to many Australians.”
Mr Turnbull, a strong same-sex marriage supporter, is facing debate within his government over what the parliamentary bill should include.
Some conservative MPs are pushing for the bill to include exemptions that would allow businesses opposed to same-sex marriage to refuse goods and services for weddings.
But matters are complicated: two government politicians have proposed introducing separate bills to parliament to legislate same-sex marriage.
One bill, by Senator Dean Smith, has broad support from opposition parties and many members of the government, including Mr Turnbull.
An alternative bill, suggested by Senator Paterson, has drawn support from more conservative MPs who say it provides stronger religious protections. (Courtesy BBC)