The Grizzlies also received a second round-draft pick from the Celtics for second-year forward Roy Rogers.
In acquiring Mack, Vancouver gave up a second-round pick.
Rogers' departure came less than a week after he questioned his teammates' commitment after a 113-83 exhibition loss to the Phoenix Suns.
Hill denied that Rogers' comments had anything to do with the move, noting that the Grizzlies had been discussing the deal since the summer.
Sacramento King forward Lawrence Funderburke was suspended without pay for the opener at Vancouver and fined $2,500 by the NBA for leaving the bench area during an altercation during Friday night's exhibition against the Indiana Pacers.
Washington Bullet guard Tim Legler (pulled hamstring) will start this season the same way he did the last one--on the injured list.
Legler played only 15 games last season because of an injured right knee.