The Kings announced the latest deal Tuesday.
Sacramento first signed White to a 10-day contract March 6, and he immediately reported to the Reno Bighorns of the NBA Development League. White has started four games for Reno, averaging 8.8 points, 4.3 rebounds, 2.8 assists and 24.8 minutes per game.
White has yet to play for the Kings, who just completed a seven-game road trip. Sacramento was hosting Washington on Tuesday night.
White was drafted 16th overall out of Iowa State by Houston in 2012. He never played for the Rockets after the sides couldn't agree on how to treat his anxiety disorder, which includes a fear of flying.