The play, prompted by the recent revelations of Edward Snowden, "explores how governments and corporations collect and use our personal information, and what that means for our security, our identity and our future."
Author James Graham scored a hit in 2012 with This House, an exploration of 70s coalition politics that ran at the National Theatre.
Although details of Miller's role in Privacy, which is directed by Josie Rourke, are still to be revealed, she has obvious ties to the play's concerns, having been involved in the recent Leveson enquiry into press intrusion.
According to a recent interview with Esquire, the play will offer the actress an "eloquent and devastating riposte to her anonymous online detractors, her inky-fingered tabloid tormentors and all those individuals and organisations interested in prying into the private business of other people."
Miller was last on the West End stage in Trevor Nunn's award-winning production of Terence Rattigan's Flare Path, which played at the Theatre Royal Haymarket in 2011. Her many film credits include Factory Girl, Alfie (alongside ex boyfriend Jude Law) and Layer Cake.
Privacy runs at the Donmar Warehouse from 10 April to 31 May 2014.