The production will begin performances in November, under the direction of Dominic Cooke, artistic director of the Royal Court who is making his NT directing debut with it. Cooke, who has previously worked extensively for the Royal Shakespeare Company, is also currently represented in the West End by his production of Clybourne Park, running at Wyndham's Theatre.
Henry won the 2009 Evening Standard Theatre Award for Most Promising Newcomer for his performance as Othello, because although widely recognized for his TV work, he was a theatrical novice.
He will be joined in the company by actor Chris Jarman playing his long-separated twin brother Antipholus of Ephesus.
No further details are available yet, and booking has not yet opened.