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SA Chief Health Officer Nicola Spurrier said the fact her state had recorded no new cases was "good news for us," adding authorities had conducted more than 12,000 tests on Thursday alone.

"In terms of our cases, we now have 23 active cases, so that is a reduction," Professor Spurrier said.

"That means to me, we are getting as many people with respiratory symptoms tested as possible in our community."

The Victorian government welcomed the announcement, but said a permit was still required to enter Victoria from South Australia unless an exemption applied, adding its own decisions on borders would continue to be guided by its public health teams.

Permits can be obtained for any reason, however, people who have attended a SA exposure site are not permitted to enter Victoria unless granted approval by the Chief Health Officer.

Roving controls from Victoria Police also remain in place.

Queensland Premier Annastacia Palaszczuk announced on Wednesday that her state would also reopen to Victorian travellers on December 1. NSW opened its border to people entering from Victoria on Monday and Tasmania started allowing visitors from Victoria to enter the state on Friday.

The SA outbreak caused Western Australia, Queensland, Tasmania and the Northern Territory to close their borders to SA travellers and require any inbound passengers to quarantine for two weeks upon arrival. Thousands in SA were forced to quarantine or to isolate as a result of the cluster.

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The restrictions – which ended early when it was discovered a positive case lied to contract tracers – included closing all schools, universities, takeaway restaurants, cafes and food courts for six days.

Even outdoor exercise was banned, with people allowed to leave their homes only to get food or medical supplies, or because they were essential workers.

Authorities are investigating a pizza shop worker who has been accused of lying to contact tracers and blamed for plunging South Australians into the lockdown.