The cinematic transmission by NT Live will first be seen in Great Britain live on July 17, followed by an international broadcast to movie theaters on Oct. 23. The play is scheduled to run through Aug. 23 at Wyndham's Theatre in London.
Stephen Daldry, the Oscar-nominated filmmaker of "The Hours" who has also staged a number of plays and musicals, directed the production.
In "Skylight," Mulligan plays a schoolteacher who receives a visit from a former, much older lover. The play marks Mulligan's first return to the British stage since she appeared in the 2007 Royal Court production of Chekhov's "The Seagull," with Kristin Scott Thomas.
The production also marks another collaboration between Hare and Nighy, who have worked together numerous times, including on Hare's recent TV trilogy about the fictional MI5 officer Johnny Worricker.
"Skylight" was first performed in 1995 at the National Theatre before transferring to the West End. The current revival also stars Matthew Beard.
NT Live is an initiative by Britain's National Theatre to make stage productions accessible through cinematic broadcasts around the world.
While most of its transmissions are productions from the National Theatre, the series has also provided screenings of West End plays, including last year's "The Audience," starring Helen Mirren as Elizabeth II.