The single is the first from latest LP King Animal, the band's first studio album since 1996's Down on the Upside.
Soundgarden were one of the original founders of Seattle's grunge movement in the early 1990s, before breaking up in 1997.
The band reunited to tour and record new material in 2010, and have since played a handful of UK shows including headlining Download Festival in June, and appearing at the Shepherd's Bush Empire last Friday (November 9). The group were the first band to play the venue after it opened in 1994.
Billy Corgan recently lambasted the group for the reunion, claiming it was all about "money". Lead singer Chris Cornell defended the reunion in April, saying: "Certainly in writing and recording the new album, it feels very fresh.
"Everyone is included and an equal part of it musically and it feels very natural and expressive, and we're going in new directions we never did before."
King Animal is released in the UK and US today (November 12).
Watch the video for Soundgarden's 1994 hit 'Spoonman' below: