His contract is reportedly a one-year deal, sources told ESPN's Adrian Wojnarowski.
The veteran guard joined the Clippers last February after the Detroit Pistons bought him out.
Jackson averaged 9.5 points, 3.2 assists, and three boards while also shooting 41.3% from deep across 17 appearances for L.A. last season. He provides the club with some depth at the point behind Patrick Beverley.
The Oklahoma City Thunder drafted the now 30-year-old in 2011.