The newspaper reported the story Wednesday on its Web site. Terry is expected to receive the award at a news conference Friday.
Terry came off the bench in 63 of his 74 games played, averaging 33.7 minutes, 3.4 assists and a 36.6 shooting percentage from 3-point range.
The Mavericks won 50 games in the regular season, finishing as the sixth seed among Western Conference playoff teams. Dallas' first-round series against the San Antonio Spurs is tied at one game apiece.