The team announced the move Saturday.
The Cavs waived Jones because his $1.6 million salary would have become guaranteed Monday for the entire 2016-17 season, but sources told ESPN's Marc Stein that the possibility of a return exists if Jones clears waivers.
Jones, who was signed on the final day of the regular season, came off the bench in Game 6 and scored five straight points to slow a Golden State Warriors rally. He also drew a pair of fouls on Warriors forward Draymond Green.
The Cavs brought in the 35-year-old Jones to give them depth and another perimeter defender. He had plenty of postseason experience before joining Cleveland, and he wound up making a significant, if small, contribution.
Jones was suspended for Game 4 of the Eastern Conference finals for his punch to Toronto Raptors center Bismack Biyombo's groin in Game 3. He was also fined $80 for the punch. LeBron James told cleveland.com's Joe Vardon after that game that he would "take care" of Jones' fine.
Jones has averaged 5.4 points and 1.7 rebounds in 13 seasons. He began his career with Memphis in 2003 and has also played for Sacramento, Denver, Indiana, Dallas, Atlanta and the Los Angeles Clippers.
Information from the Associated Press was used in this report.