Benedict Andrews is to direct the former "X Files" actress in the Young Vic's adaptation of Tennessee Williams' play, the BBC said.
"Andrews' 'Three Sisters' was one of the most talked-about shows of recent years. I expect no less of this great combination of artists," said the theater's artistic director, David Lan.
"Streetcar" is about how sophisticated, but delusional and down-on-her-luck Blanche suffers a mental breakdown after moving in with her sister and her brutish husband.
Anderson previously appeared on the London stage in "A Doll's House" at the Donmar Warehouse in 2009 and "What the Night is For" in 2012, the BBC said.