The concert will take place on April 1 in the BBC's historic Radio Theatre, which reopened after renovations last June. It will be introduced by DJ Mark Radcliffe and DJ /journalist Stuart Maconie.
Radio 2 is running a competition to give away 75 pairs of tickets to the performance. There will be another competition for tickets to a matinee concert by the band at a later date.
Radiohead is also recording a series of interviews for BBC Radio 1, Radio 2 and BBC 6 Music.
The band rocked the music world last year when it decided to allow people to download its most recent album, 'In Rainbows', for a fee they thought fit. Nonetheless, when the CD was released this year, it went to number one in the charts.
The Radio Theatre was designed as a classical music venue in the early 1930s, and has played host to famous names such as Benjamin Britten and Yehudi Menuhin. In its latter-day reincarnation as a venue for pop music, the likes of David Bowie, REM and Prince have graced its stage.