The move could give the Leafs the roster and salary cap flexibility to make additions to a lineup that is currently ninth in the Eastern Conference standings.
Boyce is set to become an unrestricted free agent this summer. The 27-year-old has a goal and an assist in 17 games with the Leafs this season. He is earning $700,000 this season.
Rosehill, 26, is set for restricted free agency and has played 16 games with 21 penalty minutes. He is earning $600,000 this season.
The Leafs will call a player up from the Marlies on Saturday.