The live version was originally recorded on 25 November 2011 at The Chelsea Ballroom at the Cosmopolitan in Las Vegas.
The cover will be released by Parlophone on 2nd December and The track will also be on physical release on 7" disc, 12" heavyweight vinyl and a three-track download featuring "You're Gonna Need Someone On Your Side" and previously unreleased live tracks, in January 2014.
Morrissey already paid tribute to The Velvet Underground singer, admitting he was a major influence on his own life and music: "He has been there all my life. He will always be pressed to my heart. Thank God for those, like Lou, who move within their own laws, otherwise imagine how dull the world would be."
Have a listen to the cover below.