'This Is The Girl' features on Smith's upcoming album Banga, the follow-up to 2007's Twelve and her first album of newly-written material since 2004's Trampin'
Smith told Lauren Laverne on BBC 6 Music that the writing for the album was "stretched within a couple of years" and that some tracks "come in right along the wire that you didn't expect".
"The last little song was a little gift - a song for Amy Winehouse that I didn't expect to write," she said.
"It just came with a little poem I wrote that went beautiful with a piece of music my bass player [Tony Shanahan] wrote."
She added: "[The album was] already finished but it just came along. It's a song I wish I never had to write. I would rather she was still here."
Smith confirmed that Johnny Depp "plays some guitar" on the record, while Television's Tom Verlaine appears on two tracks.
"He's a kindred spirit in terms of aesthetics and writing and the books that we read," she said of Verlaine.
"But when it comes to his guitar playing he's beyond anyone I know - but we have such a nice alchemy.
"When I'm singing and he plays with me he is able to articulate words through his guitar phrasing. I've never known anyone who could do it like Tom Verlaine."
Last September, Smith released the career-spanning greatest hits compilation Outside Society.
Smith won the 2010 National Book Award in the non-fiction category for her memoir Just Kids, which explores her friendship with late photographer Robert Mapplethorpe.
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