Apparently not 100% finished yet, but holy shit finally
http://consequenceofsound.net/2015/10/radioheads-new-album-is-finished-band-plans-to-tour-in-2016/
Radiohead spent the month of September holed up in the studio working on their ninth studio album. It appears the sessions were a success, as guitarist Jonny Greenwood has told a Russian radio station that the band has all but finished the record.
We have finished recording of the new album but we keep reevaluating the work weve done, Greenwood told Russias Silver Radio (via Reddit). We hope well get it right soon, and after that well start planning the next years tour.
http://consequenceofsound.net/2015/10/radioheads-new-album-is-finished-band-plans-to-tour-in-2016/