The news comes as Michael Grandage Company announces two new West End shows for 2018, following their successful run of Labour of Love at the Noël Coward. Both plays will be directed by Grandage.
Turner stars as Mad Padraic, a terrorist deemed too violent to be a member of the IRA in the production. His previous stage work includes The Plough and the Stars, A Behanding in Spokane, and currently stars in the BBC TV show Poldark. Previous screen roles include The Hobbit and Being Human. The play, which premiered at the RSC in 2001, is a satire on terrorism and a reflection on the nature of political violence. It runs at the Noël Coward Theatre from 23 June until 8 September.
McDonagh's other play credits include The Pillowman, Hangmen and will debut his new play A Very Very Very Dark Matter at the Bridge Theatre next year.
Alongside The Lieutenant of Inishmore, the company will also revive John Logan's Red, in a new production based on the original Donmar Warehouse show, with star Alfred Molina returning to play the role of artist Mark Rothko. The original Olivier Award-winning production transferred to Broadway where it won six Tony Awards including Best Play.
He is joined by TV star Alfred Enoch (How To Get Away With Murder), playing a role Eddie Redmayne performed when the piece first opened in 2009. Enoch is also known for his role as Dean Thomas in the Harry Potter series, and his stage credits include Coriolanus at the Donmar Warehouse.
Logan and Michael Grandage previously worked together on the West End production of Peter and Alice.
Red runs from 15 May until 28 July with previews from 4 May.The Lieutenant of Inishmore runs at the Noël Coward Theatre from 4 July until 8 September with previews from 23 June.