The High Court of Australia dismissed separate objections by same-sex marriage advocates, who had argued the postal vote was invalid.
The survey does not have the power to make same-sex marriage legal, but it could lead to a vote in parliament.
Prime Minister Malcolm Turnbull has said the law could change this year if the vote shows majority support.
"We encourage every Australian to vote in this survey, to have their say," he said on Thursday.
The voluntary survey has drawn controversy over its A$122m (£75m; $97m) cost and fears that it will prompt hate-filled campaigns.
Australians will have from Tuesday until 27 October to cast their vote. The results are expected to be announced on 15 November.
After years of political procrastination, it looks like Australia should finally decide by the end of the year whether the law should change.
Both Yes and No campaign teams will now turn up the volume in a debate that has already become heated.
The opinion polls suggest a Yes vote will prevail - but then, as Britain's Brexit vote showed, it's wise not to try to second-guess the public.
The real question is what happens after the survey results are announced in November.
Will MPs be bound to follow the views of their electorate? Will they have to follow the party line?
The Attorney-General, George Brandis, has confidently predicted that same-sex marriage will be legal "by Christmas", but I expect a few more twists and turns along the way.
The unsuccessful challenges had argued that the vote was invalid because it was not approved through parliament. They also claimed that the Australian Bureau of Statistics did not have the authority to oversee the process.
The court withheld its full reasoning for dismissing the challenges so it could make a decision this week.
Successive polls have suggested a majority of Australians support legalising same-sex marriage.
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