Kelly began talking with the Eagles about replacing Andy Reid shortly after his Fighting Irish lost the BCS National Championship Game to Alabama on Monday. He earned coach of the year honors for the second time after leading Notre Dame to a 12-0 record.
In 22 years as a college head coach, Kelly has compiled a 199-67-2 record with Grand Valley State, Central Michigan, Cincinnati and Notre Dame. His resume includes two Division II national championships and two Big East titles.
CBSSports.com's Bruce Feldman first reported the news.
Kelly and Notre Dame athletic director Jack Swarbick issued statements following the announcement, via ESPN.com's Joe Schad and Yahoo! Sports' Pat Forde.
Schad is also reporting that the school is working toward an extension and raise for Kelly.