The four-year deal is worth $29 million, sources told Broussard.
The agreement was first reported by The Associated Press.
Adding Augustin gives new Magic coach Frank Vogel an experienced guard to play behind young starter Elfrid Payton.
The 28-year-old Augustin played 62 games with Oklahoma City and Denver last season. He averaged 7.5 points and 3.2 assists in 19. minutes per game.
Augustin was teammates for a time with new Magic forward Serge Ibaka in Oklahoma City.
Information from the Associated Press was used in this report.