Governor-General David Hurley on Monday issued the writ compelling the Australian Electoral Commission to hold the vote on October 14.
People will now have seven days to enrol or update their details to vote in the poll.
Under changes made by the government, Australians can use their Medicare card or citizenship certificate to sign up or alter details.
Postal vote applications opened on Monday, and will close a month later on October 11.
Australians will be asked to vote on constitutional recognition of Indigenous people and to enshrine a permanent advisory body called the voice.
The upcoming referendum will have the highest record for participation of any federal electoral event in Australian history.
As of June, the national enrolment rate is estimated at 97.5 per cent.
The rate of Indigenous enrolment is 94.1 per cent, and the rate of youth enrolment is 90.3 per cent.
Special Minister of State Don Farrell said enrolment has skyrocketed leading up to the referendum due to the changes.
"The numbers don't lie - younger Australians are ready to have a say, new Australians are ready to have a say, our First Australians are ready to have a say," Senator Farrell said.
"If you aren't enrolled or need to update your details, I urge you to do it now so you can be part of a historical, unifying moment by saying 'yes'."
The issue of the referendum writ came as a report by the Governance Institute of Australia found one in five Australians believe the voice is "unethical".
Asked to rate the ethics behind an Indigenous voice, 20 per cent of respondents said the proposal was either very unethical or unethical.
One in five people also said the voice would be one of the three top ethical issues next year.
Indigenous affairs is now seen as the second most challenging issue to navigate, tying with euthanasia, but behind immigration.
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