Webber's new production, "Love Never Dies," is due to open in London in March of next year.
The musical picks up a decade after the original's conclusion, and has the Phantom trading his hideout beneath the Paris opera house for the iconic Brooklyn amusement park known for its roller-coasters and hot dogs.
Webber said he wanted to produce a sequel because the conclusion of the original was too boring.
The new musical will also be staged in New York beginning in November 2010.
The original hit musical, a longtime fixture on the London and New York stages, featured elaborate staging and songs like "The Music of the Night."
Based on the French novel by Gaston Leroux, the play has been seen by more than 100 million people worldwide and has been translated into 15 languages. The album of the show has sold more than 40 million copies.
Producers say the sequel will be "a roller-coaster ride of obsession and intrigue."
(This version CORRECTS spelling of composer's name)