Morris, who's coming off his eighth season in the Association and second with the Celtics, will enter unrestricted free agency July 1. The 29-year-old forward averaged 13.9 points and 6.1 rebounds on 44.7 percent shooting in 27.9 minutes across 75 appearances this year.
Rozier, on the other hand, will be a restricted free agent, allowing the Celtics to match any offers that come his way.
The 25-year-old point guard stressed after Boston was eliminated from the playoffs by the Milwaukee Bucks in the second round that he "sacrificed the most out of anybody" on the roster and was ready for a "fresh start."
With Irving sidelined due to injury during the 2018 postseason, Rozier was inserted into the Celtics' starting lineup and helped guide Boston to within one game of a Finals berth, averaging 16.5 points and 5.7 assists in 36.6 minutes. He was moved back to a reserve role at the start of the 2018-19 campaign with Irving recovered from a procedure on his left knee.