The 6-foot-5 point guard, the 30th pick in the draft, averaged 16.3 points and 8.8 rebounds for New Mexico during his senior season.
The 23-year-old Giddens brings a reputation as a strong defender to the defending NBA champion Celtics.
Giddens said he has matured in the last few years. He pleaded no contest to a misdemeanor battery charge after being stabbed at a bar fight in May 2005 while playing for Kansas. He transferred to New Mexico, where he was suspended twice in his first season.