"So I am delighted that the TGA [Therapeutic Goods Administration] has now recommended that home testing will be available from the first of November."
But the Health Minister said it would be up to state and territory leaders whether they would allow at-home testing within their jurisdictions.
"The second thing is to ensure that each of the states and territories is in a position to accept [the at-home tests]," Hunt said.
"We've always said that the question of public health orders was a matter for the states."
More than 30 different Covid-19 tests have already been approved for supervised use, and will become available for at-home use pending approval from the TGA.
"We already have 33 tests that have been approved for use outside the home so I imagine they'll be able to be converted," Hunt said.
"My hope is [they'll be approved] as soon as possible after the first of November, but I won't put a particular date because the TGA runs an independent safety and effectiveness testing process for each test."
TGA boss Professor John Skerritt on Monday evening said the regulator was working with manufacturers, states and territories "as a priority" to ensure modifications could be made to ensure their suitability for at-home use.
"It is anticipated that 70 per cent of Australians across the country will be double vaccinated, triggering phase B of the national plan by the end of October," he said.
"Therefore a new regulation will be made… permitting the sale and use of home tests after 1 November."
He said individual tests would still require approval but the review of data provided to the TGA had "already commenced".
Rapid antigen testing is already being used in a number of settings across the country, such as in aged care homes and in some quarantine facilities.
On Monday, NCA Newswire revealed the TGA had been waiting on a "signal" from the Government to progress approvals for rapid antigen testing.
A statement from a spokesman for Hunt said the Government had "already tasked" the TGA with urgently assessing the safety and efficacy of rapid antigen testing for home use.
Asked if the delay in rolling out rapid antigen tests for home use in Australia was a deliberate strategy until there were higher levels of vaccination in the community, Professor Skerritt said: "Correct".
"If you've got someone out there in the community who's infectious and 80 per cent of people ... vaccinated, it's a hell of a big difference than if you've only got 50 per cent vaccinated," he told NCA Newswire.