The original Hamlet has been adapted for the new production by Jones alongside Steven Hoggett. The pair will also direct.
Organisers said the “fast-paced distillation” of the play would see Radiohead’s music become a critical part of the narrative.
Hail to the Thief was Radiohead’s sixth studio album and featured the singles There There, Go To Sleep and 2+2=5.
Recorded in the aftermath of the 9/11 terrorist attack in New York, the album reflected a period of fear and political turmoil.
A rock album at its core, Hail to The Thief was also somewhat experimental, and explored dystopian themes with Orwell-inspired lyrics.
“I was listening to a lot of political programmes on BBC Radio 4,” Yorke told XFM about the writing of the record.
“I found myself – during that mad caffeine rush in the morning, as I was in the kitchen giving my son his breakfast – writing down little nonsense phrases, those Orwellian euphemisms that [the British and American governments] are so fond of.”
Jones said the first time she saw Radiohead live was on the Hail to The Thief tour in 2003.
“It changed my DNA,” she recalled. “Not long after, I was reading Hamlet and listening to the album. Paying attention to the lyrics, I became aware of how many songs from Hail to the Thief speak to the themes of the play.
“There are uncanny reverberances between the text and the album. For years I’ve wanted to see the play and album collide in a piece of theatre. Eventually I shared the idea with Thom, who was intrigued.
“I wasn’t sure what we would make, but I knew I wanted to make it with Steven [Hoggett] and continue experimenting and building on work we have done together over many years.”
She added: “We’ve found that the play haunts the album, and the album haunts the play. Both reflect the internal disquiet and rage that result from despair – in particular despair arising from scrutiny of dominant power structures – whether within governments, communities, or families.”
Set in Elsinore, which has become a surveillance state, the play centres on Hamlet and Ophelia’s awakening to the lies and corruption in Denmark, gradually revealed by ghosts and music.
Organisers said the show’s cast would be announced in the coming months.
