No announcement has been made about Hurtt joining Chicago's staff, but Louisville released a statement saying Hurtt is leaving the program for an NFL position.
Hurtt, 35, was sanctioned last fall by the NCAA for violations committed as a Miami assistant.
Louisville had suspended Hurtt for the violations with the Hurricanes and he was under a two-year show-cause penalty requiring compliance updates to the sanctioning body. He leaves after four seasons with the Cardinals and helped recruit and develop players for a defensive unit that allowed 251.5 yards per game last season and produced national sacks leader Marcus Smith (14.5).
"I truly looked forward to working with Bobby Petrino at Louisville, but I feel this is a great opportunity," Hurtt said in a statement. "(Athletic director) Tom (Jurich) is always going to be important to me and my family. He stuck with me through the toughest of times, and I will always appreciate his support for me and my family."
Petrino had announced on Jan. 9 that he would retain Hurtt from the staff of former Louisville coach Charlie Strong, who left earlier this month to take the Texas job.
"We wish Clint nothing but the best," Petrino said in Thursday's statement. "He is a very good young coach and I am sure he will continue to do great things in the NFL."