Variety said Hudson will play Grizabella, the "Glamour Cat" who performs the well-known song "Memory." Details have yet to emerge about Swift, Corden and McKellen's roles.
Tom Hooper, the Oscar-winning director of The King's Speech, will direct the Cats film. The movie is scheduled to begin production in the U.K. in November.
Cats is based on the T.S. Eliot book Old Possum's Book of Practical Cats. The West End musical starring Elaine Paige as Grizabella debuted in 1981, while the Broadway version with Betty Buckley opened the next year.