Stephen Daldry's award-winning production will open at the Gerald Schoenfeld Theatre on 17 February 2015, and will run until 28 June.
Peter Morgan's play, which originally ran at the Gielgud Theatre last year, imagines a series of pivotal meetings between various prime ministers and the Queen.
Mirren is no stranger to playing the monarch, having starred in the 2006 film The Queen, also written by Peter Morgan, which garnered her an Academy Award.
The Audience is designed by Bob Crowley with lighting by Rick Fisher, sound by Paul Arditti, and music by Paul Englishby. It is produced by Matthew Byam Shaw for Playful Productions, Robert Fox and Andy Harries.
Full casting is to be announced for the production, tickets for which go onsale in September.