The stage production will be based on Richard Linklater's 2003 film, which starred Black as an energetic music teacher, and will feature music from the movie as well as new tunes written by Lloyd Webber.
The English composer says, "It is a joy for me to return to my Jesus Christ Superstar roots.
"When Deep Purple's Ian Gillan was recording Jesus for Tim Rice and me at London's Olympic Studios, Led Zeppelin was recording next door and a glimpse of a (Rolling) Stone or two was routine! School of Rock is hugely about how music can empower kids."
The show will be directed by Laurence Connor and is slated to begin previews on 2 November (15) at the Winter Garden Theatre.
Casting will begin in January (15), according to The Hollywood Reporter.