The play, which has a limited run to 23 August, first ran at the National Theatre in 1995 before being revived in 1997 at the Vaudeville Theatre.
It tells the story of a schoolteacher, Kyra Hollis (played by Carey Mulligan), who one night receives an unexpected visit from her former lover Tom (played by Nighy) and his son Edward (played by Matthew Beard).
Matthew Beard makes his stage debut in Skylight. His film credits include And When Did you Last See Your Father?, An Education opposite Carey Mulligan and One Day, Chat Room and The Look of Love. Later this year he will be seen in the film adaptation of Laura Wade's Posh, as well as The Imitation Game and Singularity.
Bill Nighy has history with the play, having performed the same role in its 1997 revival. He has also previously starred on stage in David Hare's Pravda, Map of the World and The Vertical Hour.
His myriad film credits include Love Actually, Wild Target, Pirate Radio, Valkyrie, AKA, Notes on a Scandal, Underworld and Underworld: Evolution, The Constant Gardner, Pirates of the Caribbean and Harry Potter and the Deathly Hallows.
Carey Mulligan makes her West End debut in Skylight. Her previous stage roles include Through A Glass Darkly and The Seagull, both in New York. Film credits include An Education, Inside Llewyn Davis, The Great Gatsby, Shame, Public Enemies, Never Let Me Go and Pride and Prejudice.
Skylight is directed by Stephen Daldry, who has also just been named as a board member for the PAC in New York, with designs by Bob Crowley, lighting by Natasha Katz, sound by Paul Arditti and music by Paul Englishby.