Harvey Fierstein hosted the ceremony, which toasted longtime theater industry professionals.
Mueller's Tony-nominated costars Jarrod Spector and Anika Larsen have also extended their contracts.
Bandstand is written by Robert Taylor and Richard Oberacker.
The celebration will take place on September 23.
Campbell will replace Jake Epstein in the role of Gerry Goffin.
The new musical will open in the West End at London's Aldwych Theatre in 2015.
The Broadway community will gather at Imagine: A Concert of Hope to benefit the Brian Werbel Memorial Fund.
Broadway performers will help raise money to benefit cancer research.
Neil Patrick Harris, Sutton Foster, Kelli O'Hara, Ramin Karimloo, and more traveled to the 86th floor to drink in the breathtaking view.