The Thom Yorke-fronted band retweeted the announcements by the festivals on Twitter, fuelling speculation about a new album and further tour dates, reported Digital Spy.
Suggestions about an imminent release of their upcoming ninth LP were rife when it emerged the band had registered a new company called Dawn Chorus LLP.
It follows a similar trend to the surprise release of their last two albums In Rainbows and The King of Limbs.
Radiohead will play Primavera in Barcelona alongside the newly reformed LCD Soundsystem and Sigur Ros.