The survey does not have the power to change the law but could lead to a vote in parliament.
Australian political leaders, including Prime Minister Malcolm Turnbull, have said they support the Yes campaign.
People will have until 7 November to cast their vote by mail and results of the voluntary poll are expected on 15 November.
On Sunday ahead of the ballots being mailed out, thousands of Australians rallied in support of the campaign and dressed in rainbow colours.
The No campaign said it remained confident it had strong support.