Robinson, a veteran of seven NBA seasons, averaged 11.2 points and 4.5 assists per game last season for the Golden State Warriors.
Golden State coach Mark Jackson tweeted: "The Bulls got a good one. It was a Pleasure coaching u."
In past seasons, Robinson has proven to be a prolific scorer. In 2008-09 he averaged a career high 17.2 points per a game for the Knicks. In spite of standing just 5-foot-9, Robinson also is the only player in NBA history to win the slam dunk contest three times.
Robinson likely will back up Kirk Hinrich at point guard to begin the season while Derrick Rose recovers from ACL surgery.
ESPNChicago.com's Nick Friedell contributed to this story.