A travel bubble between Tasmania and Western Australia, South Australia and the Northern Territory will be formed on August 7.
Premier Peter Gutwein said Tasmania was one of the safest places on the planet along with these three jurisdictions.
Arrivals at airports will have to undergo mandatory health checks and quarantine until test results are obtained.
Mr Gutwein said failure to take a test would mean a traveller would have to quarantine for 14 days within a government-run hotel.
He said mandatory testing for essential workers would start on July 31.
Mr Gutwein said a decision on whether to open the state to travellers from Queensland, New South Wales and the ACT will be made on August 14.
He said this means an AFL game in Hobart between North Melbourne and Melbourne, who have players based in Queensland, will not go ahead.
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