Campbell will replace Jake Epstein in the role of Gerry Goffin.
The Wing will now copresent the awards with The Village Voice.
The Broadway League had decided not to dim Broadway's marquees for the pioneering comedian.
Jarvis originated the role of Lonny in the heavy-metal musical.
Nominations will be announced in late April.
The Broadway League has decided not to afford Rivers the honor.
Menzel will work with the organization as part of the Fred Gabler Helping Hand Camp Fund.
Indigo Theatre Project's benefit event is directed by Trip Cullman.
The Drama Desk winner is the latest actor to take on the title role in the hit Broadway musical.
Tony winner James Corden, who was expected to star, will be taking over for Craig Ferguson as the host of CBS' The Late Late Show.