The show, inspired by the poems in TS Eliot's book Old Possum's Book Of Practical Cats, has been seen by more than 50 million people in more than 30 countries since its launch in 1981.
Composer Andrew Lloyd Webber said he was "never very happy" with some parts of the show, including the Rum Tum Tugger song.
He said the character would become "a street cat" in the new version, adding: "I've come to the conclusion that having read Eliot again, maybe Eliot was the inventor of rap".
He said: "The thing about the Eliot verse is that you can tell he's American."
The show, which runs at the London Palladium from December 6, reunites Lloyd Webber with its original director Trevor Nunn.