The show will play at London's Palace Theatre. The box office opens in February and the cast will be announced in the New Year.
Brown also said that Anne Hathaway is in talks to star in the project. No official casting has been announced.
Woman in White got its first airing for an audience July 11-13 at the Sydmonton Festival, the composer's private arts festival at his English country home.
The presentation was a workshop of Act One and included a couple songs from Act Two. A six-piece orchestra was conducted by Simon Lee.
The musical is freely based on the novel by Wilkie Collins and has book and lyrics by Charlotte Jones (Humble Boy) and David Zippel (City of Angels). Trevor Nunn (Cats) directed, and Simon Lee was musical director. The cast included Hathaway ("The Princess Diaries"), Laura Michelle Kelly (Eliza of Trevor Nunn's West End My Fair Lady), Kevin McKidd ("Trainspotting"), Roger Allam ("The Roman Spring of Mrs. Stone") and Kevin Colson (Aspects of Love).
A mysterious tale of damsels in distress, a wicked aristocrat, lunatic asylums, family fortunes, desolate mansions and a sinister Secret Society, "The Woman in White" was a popular success for 19th-century English novelist Wilkie Collins, who went on to write the first modern detective story, "The Moonstone."
The musical continues to develop toward a production, but there is no announced timetable for the work. American and British producers and other industry folk were present at Sydmonton.
Andrew Lloyd Webber composed Evita, The Phantom of the Opera, Jesus Christ Superstar, among others, and produced Bombay Dreams on the West End.
Bombay Dreams, the Bollywood-flavored show with a score by composer A.R. Rahman and lyricist Don Black, will be produced on Broadway by Waxman Williams Entertainment in early 2004. Lloyd Webber's long-running Broadway musical, The Phantom of the Opera, continues at the Majestic.