He was also best known for performing the theme song to the 2006 James Bond movie Casino Royale, You Know My Name.
In a statement, Chris Cornell’s representative Brian Bumbery said his death was “sudden and unexpected”.
The statement also also said the family would be working closely with the medical examiner to determine the cause and asked for privacy.
Chris Cornell died shortly after playing a concert with Soundgarden in Detroit on May 17.
The show was part of a wider tour and the group had a number of live dates scheduled for later this month.
Elton John led the tributes, tweeting: “Shocked and saddened by the sudden death of @chriscornell. A great singer, songwriter and the loveliest man.”
Led Zeppelin guitarist Jimmy Page added: “RIP Chris Cornell. Incredibly talented, incredibly young, incredibly missed.”
Chris Cornell was born on July 20, 1964.
As a solo artist, Chris Cornell released four studio albums – most recently 2015’s Higher Truth.
2006’s You Know My Name, which was the theme song to Casino Royale, made him the first male American artist to write and perform the theme song for a James Bond movie.
However, he was perhaps most famous as the lead singer of Seattle band Soundgarden, which formed in 1984 and went on to release six studio albums.
In 2016, Soundgarden confirmed they were returning to the studio to record new material and a tour was announced for this year.
On May 17, the Fox Theatre in Detroit tweeted pictures of the band while they were live on stage.
Chris Cornell himself tweeted about the show that evening, writing: “Finally back to Rock City!”
In 2001, Chris Cornell joined rock Audioslave, which consisted of Cornell on lead vocals, together with Rage Against The Machine members Tom Morello, Tim Commerford and Brad Wilk (drums).
Audioslave released three albums, but disbanded in 2007.
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