A highly-touted prospect coming out of high school, the 6'4" Greene originally chose to attend the University of Florida, his hometown college. However, after a couple of years Greene became dissatisfied with his playing time and decided to transfer to the University of Louisiana at Lafayette where he became known in the Sun Belt Conference for his aggressive play, winning the Defensive Player of the Year award his senior season.
Greene came into the 2005 NBA Draft far under the radar, and it came as a surprise to some analysts when he was taken as a second round pick (53rd overall) by the Boston Celtics, despite the fact that Celtics' director of basketball operations Danny Ainge had been eyeing him for some time.
The point guard was originally expected to have to fight for his roster spot coming into the 2005 season, however his strong play in the preseason vaulted him into second on the depth chart behind Delonte West to begin the season. His status as the backup point guard was cemented by a season-ending injury to Dan Dickau and the trade of Marcus Banks to the Minnesota Timberwolves.
On March 29, 2006, Greene was suspended by the Boston Celtics for one game after he was charged with driving his sport utility vehicle at more than 90 mph on a street in suburban Boston.