Tasmania is expected to lower its borders to people from Victoria on November 27.
The reopening date had previously been scheduled for December 1.
Premier Peter Gutwein on Wednesday told Parliament Victoria was now considered a medium-risk area due to having no new COVID-19 cases diagnosed for 12 consecutive days.
He said as a result of that, the indicative border reopening date could be brought slightly forward and quarantine requirements for people entering the state from Victoria could change.
"Victoria is a very important part of the overall country's economy and it's also a very important part of the social fabric for many Tasmanians with family and friends there," Mr Gutwein said.
From Friday, people entering Tasmania from the state can quarantine at home or a suitable dedicated residence, rather than in a government hotel.
Travellers from all other states and territories can visit Tasmania without the need to go into quarantine.
Public Health director Mark Veitch praised the response of the Victorian Government, its public health agencies and the community on containing the state's coronavirus outbreak.
"Victoria has actually achieved something extraordinary in bringing their outbreak of coronavirus under control," he said.
"[They've] achieved something few places in the world have managed during this pandemic."
Launceston Airport chief executive Hans van Pelt said an earlier border reopening date was welcome news.
"The reopening of the Tasmania-Victoria border is huge as it unlocks travel with our largest inbound tourism market," he said.
"The Launceston-Melbourne route is our busiest and we expect bookings to take-off now that people in both states have a confirmed date to work with."
Mandatory contract tracing starts on Friday whereby venues must keep a list of patrons who visited the premises for 28 days.
People will be able to stand while drinking alcohol outdoors at venues from that day.