Governor Kate Warner has put her cancer behind her and will stay on in the vice-regal role for another year.
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Professor Warner said she was thrilled to have the extension and believed she had the "energy and enthusiasm" for another year in the job.
She said she did not believe she could continue at her current pace for another five years.
"I'm glad to have the cancer thing behind me and I'm well again," she said.
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"I'm now 71 and it's a busy job. I'm usually in the office by 8 o'clock, sometimes we have things earlier, and most days we don't finish until 7 o'clock.
"I managed very well last time but I've had friends with cancer and I know that the longer you have the treatment for the more difficult it is.
"It was really minimal disruption to my duties."
Professor Warner, who was appointed Tasmania's first female governor for a five-year term in 201,4 was diagnosed with stage four non-Hodgkin Lymphoma in January this year.
She has been given the all clear but has to have regular three monthly checks.
Professor Warner said she loved the variety of her role and meeting many different Tasmanians.
"It really amazes me how pleased people are to meet the Governor and how they feel it adds something to the occasion when you are present," she said.
"That was something I haven't really appreciated until I was in the role. I love visiting schools and talk to the kids, the huge variety of people we meet is the highlight."
Premier Will Hodgman said Her Majesty the Queen had given formal approval to his request to extend the term of office until December 9, 2020.
"I'm delighted she is staying on because she is held in such high regard by the people of Tasmania," Mr Hodgman said.
"Her Excellency has fulfilled her constitutional, ceremonial and community roles with great distinction since her appointment in 2014, and both Her Excellency and Mr Warner are held in the highest regard by the people of Tasmania.
I am very pleased Her Majesty has approved the extension of the term of the Honourable Kate Warner AC, as Governor of Tasmania, and on behalf of the people of Tasmania extend our best wishes to Her Excellency and Mr Warner.