Armitage, best known for his work on screen, including Robin Hood, Spooks and Peter Jackson's Hobbit trilogy, will play John Proctor in Yaël Farber's production, which previews from 24 June.
The Crucible is set in the town of Salem, Massachusetts, where in 1692, 19 adults and two dogs were hanged for witchcraft, and one man was pressed to death for refusing to plead. The play tells the story of one man's fight to save his identity in a repressive Puritan community.
Miller's play was inspired by the actions of The House Committee on Un-American Activities of the McCarthy era, in front of which the playwright was invited to give evidence.
It was most recently seen in London at the Open Air Theatre in 2010, with Patrick O'Kane as Proctor.
Joining Armitage in the cast at the Old Vic will be Anna Madeley (Earthquakes in London) as Elizabeth Proctor and newcomer Samantha Colley as Abigail Williams.
The cast also includes Sarah Niles, Rebecca Saire and Zara White.