The new production will be called "Love Never Dies." It is due to open in London in March of next year. The musical will also be staged in New York beginning November 2010 and will open in Australia in 2011.
The musical picks up a decade after the original's conclusion, and has the Phantom trading his customary hideout beneath the Paris opera house for Coney Island, the iconic Brooklyn amusement park known for its roller coasters and "Nathan's Famous" hot dogs.
Webber said he wanted to produce a sequel because the conclusion of the original was too boring.
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," and "All I Ask of You."
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 and staged in 25 different countries, including Brazil, China and Poland.
The album of the show has sold more than 40 million copies.
Producers say the sequel will be "a rollercoaster ride of obsession and intrigue." It is set 10 years after the Phantom's mysterious disappearance from Paris.
Few details were released Thursday, but a new official Web site devoted to the sequel shows an early trans-Atlantic ocean liner making a voyage across the sea.
Tickets for the London shows at the Adelphi Theatre were placed on sale Thursday and fans were also told they could pre-order the album of the show's tunes.