The show will play for twelve weeks at the Lloyd Webber-owned London Palladium, opening on 6 December 2014 following its current UK tour.
It's the first time the dance musical, adapted from Old Possum's Book of Practical Cats by TS Eliot, has been seen in the West End since it closed at the New London Theatre in 2002 after a 21-year run.
Speaking to press on the stage of the Palladium today, the composer said he is revising the show for the Palladium run, including a "completely rewritten" version of "Growltiger's Last Stand".
"Our main focus is to get a new edition of Cats - a new blueprint, if you like," Lloyd Webber said.
He also revealed he is reworking the character of the Rum Tum Tugger, originally played by Paul Nicholas, as a "street cat" who will rap.
Answering a question about the number of revivals currently in the West End, Lloyd Webber retorted: "If you said that [there were too many revivals], we wouldn't have a lot of room for Shakespeare, would we Trevor?," gesturing to Nunn, a previous artistic director of the Royal Shakespeare Company.
To help entice a younger generation, and to reflect the fact the show is running over Christmas, Lloyd Webber said there will be make-up artists to paint children's faces and photo booths in the Palladium foyer during the run.
Nunn, who subsequently worked with Lloyd Webber on Starlight Express, Sunset Boulevard and The Woman in White, told WhatsOnStage he remembers the atmosphere around the original production of Cats as being "rather threatening".
"A number of reviewers at the time thought it was very bad form for somebody who was largely concerned with the classical theatre to become involved with musicals," he said. "We knew we were doing something original with Cats, but whether it would have mass popularity nobody could have predicted."
The Palladium run is produced by David Ian and Really Useful Theatres, and also features work by original designer John Napier, who Nunn called a "genius".
Cats is not the only Lloyd Webber revival hitting the West End this year - Evita is being staged at the Dominion Theatre from September.
Nunn said this was not necessary indicative of a decline in new work. "The future of music theatre is as unpredictable as it always has been - it goes up and down... [playwright] George S Kaufman used to talk about theatre as the 'miraculous invalid', in that we're all at the death bed shaking our heads, but before we know it the invalid has leapt out the bed and is doing a dance routine."
Choreographer Gillian Lynne - who was made a Dame last year - told WhatsOnStage that the chance to revisit Cats is a "joyous event".
"It's not going to be a new show - it would be stupid to make a version of something that is still popular around the world," she added. "But it will be a show enriched."
Booking for Cats opens today - for more info and tickets click here