The producer revealed that he initially refused to work on the star's latest collection Lioness: Hidden Treasures, which topped the UK chart on Sunday (December 11).
However, he changed his mind after hearing Winehouse's vocal recording for 'Will You Still Love Me Tomorrow' and realised it was something "special".
Ronson told BBC Breakfast that Lioness is "an insight into the songs she loved", adding: "She really was an encyclopaedia of these old jazz and soul standards. She could pick up a guitar and play any of them."
He continued: "I didn't know if they necessarily needed what I had to give and it was a bit soon for me to spend that time listening to her voice on a loop, like you do when you're in a studio working on a record.
"Then I heard this vocal she'd recorded for 'Will You Still Love Me Tomorrow' and I thought, 'This is really special and I want to be a part of this and make one more piece of something magical with Amy'."
Mitch Winehouse recently claimed that Lady GaGa should play his daughter in a biopic of her life.
> Amy Winehouse boyfriend Reg Traviss asked to direct biopic
Watch the music video for Amy Winehouse's 'Our Day Will Come' below: