The cover, performed by a variety of local community music groups, will be entered into the official UK singles chart and is available for download, with the hope that it will go on to become Christmas number one, the supermarket said.
Proceeds from each download will go to the Co-op Foundation, a charity that helps young people beat loneliness.
The film, which includes flashes of the Co-op Christmas food range, will air on Channel 4 and ITV this evening (1 December). It has also been released across social media.
Amanda Jennings, Co-op marketing communications director, said: "Christmas is about togetherness and we have chosen two of the great unifiers - food and music - to showcase this and bring Christmas back to what really matters. It's all about those little moments that bring people together at Christmas."
PR for the campaign is handled by DawBell.