Arizona State announced the hire Tuesday. The Bengals fired Lewis in December after a 16-year tenure as coach of the AFC North franchise.
Edwards was hired as the Sun Devils' football coach in 2017. He was an NFL head coach for eight years before returning to the college ranks.
"Marvin Lewis is one of the most respected minds in our game," Edwards said in a release from the school. "Whether as the winningest coach in the franchise history of the Cincinnati Bengals, or the architect of one the greatest defenses in NFL history, the 2000 Baltimore Ravens, Marvin has succeeded everywhere he has been and he has done it the right way."
"His passion for teaching will be an incredible benefit not only for our coaches, but also for the young men we are responsible for as students and athletes."
Lewis led the Bengals to a franchise-record 131 wins, but never won a playoff game during his tenure with the team.
"I've known Herman for almost 30 years and the opportunity to come and assist him and his coaches win football games is very exciting and appealing," Lewis said. "Arizona State and Tempe have always been special to me."
The Sun Devils posted a 7-6 record in 2018 after also going 7-6 in 2017.