Frontman Thom Yorke, who is working with Tony- and Olivier Award-winning designer Christine Jones and director Steven Hoggett, said in a statement it was an "interesting and intimidating challenge"
Shakespeare will meet Radiohead in a new stage production of "Hamlet" due to premiere next year, set to a reworked version of the band's "Hail to the Thief" album.
Alternative rockers Radiohead had a string of best-selling singles in the 1990s and early 2000s including "Creep", "Paranoid Android" and "No Surprises".