Kirby reunites with Anderson having appeared alongside her in the BBC's adaptation of Great Expectations, also starring Ray Winstone and Douglas Booth.
Her stage credits include the 2011 première of Anya Reiss' The Acid Test at the Royal Court Theatre, Masha in Three Sisters at the Young Vic in 2012 and Isabella in the 2013 National Theatre production of Edward II.
Ben Foster has appeared in films including Get Over It, X-Men: The Last Stand and Alpha Dog, and had a recurring role in the HBO Series, Six Feet Under.
For his theatre debut he took over from Shia LaBeouf in the Broadway play Orphans in 2013.
The production runs from 23 July - 6 September 2014 and is helmed by radical Australian director Benedict Andrews, who staged Three Sisters at the venue in 2012.
The play, which successfully transferred to the big screen in 1951 and made a star of Marlon Brando, centres on fading southern belle Blanche DuBois (Anderson), whose arrival at the home of her sister Stella (Kirby) and her brutish husband Stanley Kowalski (Foster) upsets their marital dynamic and sets Blanche and Stanley on a violent collision course.
Anderson made her West End debut in 2002 in the world premiere of Michael Weller's two-hander What the Night Is For alongside Roger Allam, for which she won a WhatsOnStage Award. Her subsequent London stage appearances include The Sweetest Swing in Baseball at the Royal Court and A Doll's House at the Donmar Warehouse.