Weatherald, 28, did not play for South Australia since last December having stepped away from the game to manage his mental health early in the BBL.
"I'm really excited and grateful to the Tigers for this opportunity," Weatherald said. "I'm obviously also incredibly thankful to South Australian cricket for giving me my start and my initial opportunity, but I'm looking forward to embracing a new environment and continuing to learn so I can continue to grow my game in the coming years."
"I'm 28 and think I still have the opportunity to take my game to another level, so I'm looking forward to getting that journey underway in Hobart shortly."
He will remain with Adelaide Strikers in the BBL where he has two more years on his contract.
At Tasmania he will add to the team's top-order options which includes Australia A duo of Caleb Jewell and Tim Ward.
"We're really excited about securing Jake's services for at least the next two years," Jeff Vaughan, Tasmania's head coach, said. "It was a really great opportunity that came to us during the contracting period that can only be seen as win-win for both parties."
"We think Jake can bring some valuable experience and cricket IQ to our top order across both the white- and red-ball formats of the game but is also at an age where he can continue to develop his game and improve."
Tim Nielsen, SACA's head of performance, thanked Weatherald for his eight years with the state.
"Jake has been a big contributor to Redbacks cricket for many years and we thank him for all his efforts," he said.
"Jake identified a fresh start as an important part of his career moving forward and SACA are supportive of this new, exciting opportunity in front of him.
"The most important thing for Jake is that he is happy, healthy and playing cricket and we hope this new chapter goes well for him."
South Australia, along with the other states, will confirm their full lists for the 2023-24 season in the coming weeks.