"Velvet" was released as a digital download and on 7-inch vinyl on April 20, 2009, and was later included on their debut album A Brief History of Love in September 2009.

Pitchfork Media described "Velvet" as "undeniably immense, but it's a tribute to the Big Pink's skill and maturity that it still manages to sound intimate," and awarded the track a 7 out of 10 rating.

[4] In August 2009, "Velvet" was included on Pitchfork's Top 500 Tracks of the 2000s list, voted in at number 500.

[7] Remixes by Mount Kimbie and Van Rivers & The Subliminal Kid (producers for Fever Ray) were also commissioned.

The song was commonly covered by Swedish artist Lykke Li during her 2011 Wounded Rhymes Tour.