General manager Billy King did not release terms of the contract, but a person with knowledge of the deal said Graham received a partially guaranteed contract for this season with a team option for next year. The person did not want to be identified because he was not authorized to speak for the team.
King also announced the hiring of Doug Overton as a player development coach and Robby Hoenshel as an assistant athletic trainer and director of sports rehabilitation.
A five-year veteran, Graham has career averages of 4.3 points and 1.7 rebounds in 180 career games with Cleveland, Chicago, Houston, Portland, Indiana and Charlotte. He appeared in a career-high 70 games with the Bobcats last season, averaging 4.2 points and 1.9 rebounds.
Overton takes on a new role in player development after spending the past two seasons as an assistant coach. The 11-year NBA veteran will assist the players with individual skills on the court.
Hoenshel comes to the Nets after working at the Jacksonville Orthopedic Institute, where he served as a physical therapist.