Holiday, 28, averaged 7.7 points and 2.7 rebounds per game for the New York Knicks last season.
The Knicks, according to sources, didn't make a competitive offer for the 6-foot-6 guard.
Holiday, a four-year veteran, was also being pursued by the Minnesota Timberwolves. He showed last season in New York an ability to defend well on the perimeter and knock down perimeter shots.
Holiday can fit in at shooting guard or small forward for Chicago, which appears to be in the process of rebuilding its roster.
The agreement between Holiday and the Bulls was first reported by The Vertical.