Mr Morrison said Australia’s mandatory 14-day hotel quarantine – which costs each traveller A$3,000 (£1,600; $2,100) – would be replaced by seven days of home quarantine for vaccinated Australians or permanent residents.
Unvaccinated travellers must still quarantine for 14 days in hotels.
Australian carrier Qantas responded by announcing it would restart its international flying a month earlier. It had already put flights to major overseas destinations on sale from 18 December.
Sydney, Melbourne and Canberra are currently in lockdown due to outbreaks of the virus.
That has helped prompt a surge in the vaccine uptake in recent months.
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New South Wales – which includes Sydney – is on track to be first state to cross the 80% threshold, in a few weeks. Victoria – containing Melbourne – is not far behind.
But states such as Queensland and Western Australia have threatened to keep their borders closed until vaccine rates are even higher.
These states have managed to maintain Covid rates at or near zero, after shutting their borders to states with infections.