Fickell, who took over at Cincinnati in 2017, has led the Bearcats to back-to-back 11-win seasons. He was named Coach of the Year in the American Athletic Conference in 2018. He also served as interim head coach at Ohio State in 2011 when the Buckeyes went 6-7.
Should Fickell leave Cincinnati for another job before the end of this year, he would reportedly owe the university a $2 million buyout.
Athletic director Bill Beekman praised Dantonio for his "outstanding leadership" during his 13-year tenure.
“As the all-time winningest coach in school history, he’s raised the bar for Michigan State football," Beekman said in a statement. "He’s mentored young men and led them to success on the field, in the classroom and in life, while serving as a great ambassador for Michigan State University.
"As we begin the search for Mark’s successor, we will look for the right fit who will continue the success at both the conference and national level."