The Therapeutic Goods Administration said on Monday it would recognise the Indian-made Covaxin and the Chinese-made BBIBP-CorV vaccine.

In a statement, the administration said the decision would allow those who had been jabbed with either of the vaccines to be eligible for travel to Australia.

Only travellers who have been fully immunised with a vaccine recognised by the administration will be able to arrive in Australia under travel arrangements.

"This will have significant impacts for the return of international students, and travel of skilled and unskilled workers to Australia," an administration spokesman said.

"Citizens of China and India as well as other countries in our region where these vaccines have been widely deployed will now be considered fully vaccinated on entry to Australia."

It comes as international arrivals touched down in Australia without having to undergo quarantine, for the first time in almost two years.

Monday saw fully vaccinated Australians being able to arrive back in Sydney and Melbourne for the first time since the pandemic began.

There were tearful scenes at airports, with many families able to be reunited after more than a year of travel being restricted

While international travel is currently limited to fully vaccinated citizens, permanent residents and their families, it's expected skilled workers, those on visas and then tourists will be allowed to enter in coming months.

Prime Minister Scott Morrison said Australia was again open to the world, following a rise in vaccination rates.

"The Australian public have been keeping their side of the deal, which means the national plan is enabling them to regain the things that COVID has taken from them," he said.

It comes as quarantine-free travel arrangements resumed with New Zealand, after the travel bubble was suspended earlier this year following the Delta variant outbreak.

Australians will also be able to travel to Singapore from November 8, while residents from the Asian city state will be able to come to Australia from later this month.

Treasurer Josh Frydenberg said the resumption of international travel and the easing of COVID restrictions across the country would likely lead to a spike in hospitalisations and deaths from the virus.

"That is ultimately what happens when you live with the virus, and there are no other options," he told reporters in Melbourne.

"We can't live in lockdown and closed borders forever and live without our freedoms, and it's why it's important to ease restrictions and get on and live our lives in a COVID-safe way."

There were more than 85,000 COVID vaccines administered nationally on Sunday, with 77.5 per cent of over-16s being fully vaccinated and 88.3 per cent having had their first dose.

Victoria recorded a spike in the number of new cases on Monday, with 1471 new infections and four deaths.

In NSW, there were 135 new cases and four deaths, while there were two deaths in Canberra.

The national capital registered five new infections on Monday, the lowest number of daily cases since mid-August.

Australian Associated Press