The pair started working on the song in 2008, with the track set to appear on a forthcoming tribute album to legendary producer Quincy Jones. It was Jones‘ first hit single as a producer, and a version by Dave Stewart and Barbara Gaskin topped the UK charts in 1981.
A release date for the album is yet to be set.
Ronson told BBC Newsbeat that Winehouse “sounds brilliant on it”.
He added: “It’s quite funny to come off of my album where the whole tag line, or thing we told ourselves, was no covers, no horns and then to do a very Amy-sounding record like that.”
Ronson‘s next solo album ‘Record Collection’ will be released as Mark Ronson And The Business INTL. in September.