The song - released next month - was premiered by DJ Chris Moyles on Radio 1 this morning.
Cole's official website has also been updated with images from the music video, which show the X Factor judge in a ballet dress with a male dancer wearing black.
The first official issue of the X Factor Magazine describes the video as "gothic ballet".
Her website also revealed that it will sell an exclusive "special version" of her forthcoming album, due for release in November.