News of Mr Rundle's death, aged 86, was shared on Sunday by Liberal colleagues including Tasmanian Premier Jeremy Rockliff.
"Tony was intelligent, kind and considered - a remarkable man, leaving a positive legacy," Mr Rockliff said.
Mr Rundle served as an MP in Tasmania for 16 years, including as premier from 1996 to 1998.
He was in power when 35 people were killed in a shooting spree at Port Arthur and oversaw Tasmania's subsequent widely-lauded gun law reform.
Tasmanian Liberal senator Richard Colbeck said Mr Rundle was a keen sailor, a Rotarian and a strong and considered leader for his community for many years before he was elected to parliament.
"Tony led changes that endure today and for which Tasmanians are better off," he said.
"First amongst those was his leadership following the Port Arthur massacre, an enormously distressing time for Tasmanians and Australians alike.
"Tony led the aftermath with great dignity and empathy and set the state on the path to recovery."
Senator Colbeck said Mr Rundle also oversaw gay law reform, the development of Basslink, the signing of the Regional Forest Agreement and commissioned the Nixon Review of the Tasmanian economy.
Tasmania also became the first state to make a public apology to the Stolen Generations during Mr Rundle's time as premier.
Former prime minister John Howard, who worked closely with Mr Rundle in the wake of the Port Arthur tragedy in April 1996, said he was a fine premier and "a true gentleman".
Mr Howard said the massacre shocked the nation and was keenly felt by the Tasmanian community.Â
"Tony Rundle's dignified and compassionate yet firm response was reassuring to his fellow Tasmanians," he said.
Mr Rundle is survived by his wife Caroline and daughters Helen and Jane.
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