Prigioni agreed to the deal in principle two weeks ago with the Clippers, who signed the Argentine veteran for the veteran's minimum of $981,000.
The 38-year-old Prigioni averaged 4.1 points, 1.8 rebounds and 2.6 assists last season for the New York Knicks and Houston Rockets. He signed with the Knicks in 2012 after a lengthy career in Spain and Argentina.
Houston traded Prigioni to Denver last month, and the Nuggets waived him.
Prigioni played well against the Clippers in the second round of the playoffs last season, particularly impressing coach Doc Rivers with his defense. Prigioni also could back up Chris Paul as a point guard.
The Clippers have 14 players under contract for next season.