Molnar was introduced at Gillette Stadium in Foxborough, where UMass will play its home games beginning next season. The program is transitioning to the Football Bowl Subdivision, where it will compete as a football-only member in the Mid-American Conference next season.
Molnar, 50, has coached for 28 seasons, including three different stops at MAC schools -- Eastern Michigan, Western Michigan and Central Michigan. He has worked the last six seasons under Brian Kelly, at Central Michigan, Cincinnati and Notre Dame.
Molnar will continue to coach the Irish through the Dec. 29 Champs Sports Bowl.
Morris was fired Nov. 21 after a 16-17 record in three seasons as coach of the Minutemen.
Matt Fortuna is a writer for ESPNBoston.com.