Victoria, which imposed a tough lockdown after a surge in cases, has reported no new infections since the beginning of November.
The state is also relaxing its rules on wearing face masks.
Australia has recorded about 900 deaths and 28,000 infections in total.
The country has relied on lockdowns, widespread testing and aggressive contact tracing to push daily infections nationwide close to zero.
Australia shut down its international borders early in the pandemic and requires all arriving travellers to spend two weeks in quarantine in designated hotels.
The border between Victoria and NSW - the two most populous states - was closed in July as infections soared in Victoria's state capital, Melbourne.
Flights between the city and the NSW capital Sydney - normally one of the world's busiest routes - were cancelled. NSW authorities have since been in charge of guarding border crossings.
Melbourne saw cases surge to more than 700 a day in July. It has recorded 90% of the country's Covid-related deaths.