The show, which opens in July, stars the already announced Sienna Miller as Maggie, Colm Meaney as Big Daddy and Jack O'Connell as Brick.
Joining them will be Lisa Palfrey as Big Mama, Hayley Squires as Mae, Brian Gleeson as Gooper, Richard Hansel as Doctor and Michael J Shannon as Reverend.
The production opens at the Apollo Theatre on 24 July, with previews from 13 July. Australian director Andrews directs the piece which is Tennessee Williams' Pulitzer Prize winning play which premiered on Broadway in 1955.
The piece tells of a Mississippi family in crisis who gather to celebrate the birthday of cotton tycoon Big Daddy.
Cat on a Hot Tin Roof runs at the Apollo Theatre from 24 July to 7 October with previews from 13 July.