The Oscar-nominated actress will also be reunited with Matthew Beard - one of her co-stars from the movie An Education - in the production.
They will appear in a major revival of the David Hare play Skylight which is to be staged at London's Wyndham's Theatre, opening on June 18, to be directed by Billy Elliot film-maker Stephen Daldry.
Nighy - whose screen roles have included The Best Exotic Marigold Hotel and Pirates Of The Caribbean films - previously starred in Skylight 17 years ago and has had a long association with Hare's productions.
Mulligan has previously acted on stage in New York, and appeared on Broadway in Chekhov's The Seagull. She plays teacher Kyra whose former lover (played by Nighy) turns up out of the blue and they find they disagree on almost everything.
Beard, whose other roles have included One Day and The Look Of Love, is making his stage debut.
Skylight was first staged at the National Theatre in 1995, winning an Olivier Award for best play.