Critics have been swift to criticise the band because of their trenchant anti-capitalist stance, which has seen them provide their own marquee on tour so they could avoid having a logo plastered all over it.
The band's public relations firm, Hall or Nothing, defended the move saying that the band was approached by the IoC and agreed on the understanding that no corporate branding or logos appeared in the ad with the Radiohead track.
The IoC hopes that by using the Radiohead track I Might Be Wrong, from the band's new album Amnesiac, along with clips of extreme sports such as snowboarding and freestyle skiing, the competition will appeal to a younger audience.
French dance act Daft Punk has also donated the use of their music and actor Robin Williams has provided the voiceover for some of the English-language TV ads.
The campaign, called "Winter celebrates humanity", was created by TBWA\Chiat Day.