The Samoa international originally signed on a short-term contract until the end of the season but has earned a more permanent deal after impressing the coaching staff at the west-country club.
"I am very pleased that I will be staying with Bath Rugby," the 22-year-old said.
"I enjoy playing rugby with the other guys here and there are a lot of experienced international level players around who I can learn a lot off."
Bath head coach Brian Ashton added: "It is good news Jonny has signed a two-year contract.
"He has already played Test-match rugby for Samoa and I look forward to his unique style of rugby helping Bath in the future."