The state recorded 92 new COVID-19 cases on Thursday and the first virus-related hospitalisations since its borders reopened a fortnight ago.
The fresh infections are a daily record and take the number of overall active cases in Tasmania to 386.
There are two cases in hospital but none are in intensive care.
After attending national cabinet on Thursday, Premier Peter Gutwein announced several changes to the state's testing rules.
From 12.01am on January 1, travellers to the state must take a rapid antigen test 24 hours before their arrival. Queensland and South Australia have also scrapped PCR test requirements.
"If your result is positive you cannot come," Mr Gutwein told reporters in Hobart.
The test result must be declared by travellers on the state's Tas e-Travel border pass system.
Evidence of the test will not be required at the border, however anyone who lies will face a fine.
Travellers arriving in the state will be given another rapid antigen test kit at the border to carry with them in case they develop symptoms or become a close contact.
The state had required travellers to take PCR tests 72 hours before arrival since reopening its borders earlier this month, adding to long queues at interstate testing sites.
In further changes announced on Thursday, Tasmanians who travel interstate for seven days or fewer will not be required to get tested upon their return unless they are symptomatic.
Additionally, to ease pressure on testing sites, only those with COVID-19 symptoms or a positive RAT test will be able to get a PCR test.
Two free rapid antigen testing sites, at Rokeby and Glenorchy, will be set up in coming days but they will not operate as walk-up testing sites.
"I want to stress - please do not just turn up to these sites," Mr Gutwein said.
"Health will prioritise who is eligible for a rapid antigen test and will contact those people directly and arrange for them to turn up and receive tests at the locations that are being established."
Tasmania currently has half a million rapid tests available, with another two million arriving over the next month.
The majority of the state's cases, 178, are being managed at home, while there are 74 people in community clinics.
Meanwhile, St Ann's aged care facility in Hobart was forced into lockdown on Wednesday after a staff member who had worked there on Christmas Day tested positive.
Mr Gutwein said initial tests results from staff and residents had come back negative.
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