The band will perform their only Spanish show of 2012 at the festival, which takes place from July 12 to July 14 on top of a hill overlooking the city of Bilbao.
Three-day early bird tickets to the festival are available from December 14 until January 24 priced at £73, which includes camping.
More acts will be announced on Bilbao BBK Live's website soon.
Previous headliners at the event have included Coldplay, Pearl Jam, Depeche Mode, Jane's Addiction, Red Hot Chili Peppers and Suede.
Radiohead recently unveiled three new remixes of tracks from this year's The King of Limbs album.
Frontman Thom Yorke has also confirmed that the band will tour next year in support of their latest album.
> Radiohead promise indoor venues for 2012 tour
Watch Radiohead's video for 'Lotus Flower' below: