The 27-year-old didn't play for his home state of Queensland in last season's Sheffield Shield and was left off the Bulls' contract list for 2024/25.
Kuhnemann, who has 20 first-class matches under his belt, played three Tests for Australia in India in early 2023.
After being flown over mid-tour, the left-arm finger spinner took 5-16 in his second Test to help Australia beat the hosts at Indore.
"I'm very grateful to be given the opportunity from Tasmania to join their talented squad," Kuhnemann said on Monday.
"I'm excited to get down there, challenge myself, and help contribute to winning games and competitions for Tasmania."
Kuhnemann will be eyeing a spot in Australia's Test squad for their tour of Sri Lanka in February, after a summer series on home soil against India.
He will also be available for 50-over selection for Tasmania and remains contracted to the Brisbane Heat in the Big Bash League.
"We are excited to have a player of Matt's calibre join the Tigers and believe he will play a key role for usin the white-ball format of the game," Cricket Tasmania high-performance manager Salliann Beams said.
Tasmania lost to Western Australia in March's Sheffield Shield final, with Jarrod Freeman (18 wickets at 46) their first-choice spinner for the season.
Kuhnemann, who has also played four one-day internationals, was stuck behind leg-spinner Mitchell Swepson, who took 30 wickets for the season for Queensland.
Along with former Test opener Joe Burns, he was left off Queensland's contract list after the Bulls finished bottom of the ladder in the recently completed Shield campaign.
The Tigers also announced the signing of 22-year-old Queensland quick Will Prestwidge, who played two one-day games for the Bulls across three summers.
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