Vujacic is expected to meet the Clippers in Denver for a Monday night game against the Nuggets.
Vujacic has been playing in the Turkish league for the last few seasons and was last on a New Jersey Nets team that finished 24-58 by the end of the 2010-11 season. He averaged 11.4 points, 2.3 assists and 3.3 rebounds per game that year, his most productive.
The Slovenian is most well-known for his six-plus seasons with the Los Angeles Lakers, where he earned the nickname "The Machine" while coming off the bench from 2004-2011.
Now, Vujacic joins Doc Rivers' team, which is hoping point guard Chris Paul can return from a shoulder injury in the next few weeks and before the All-Star game. Where Vujacic fits in remains unclear with Darren Collison, Jared Dudley, J.J. Redick, Willie Green and Jamal Crawford eating up so much time in the backcourt.