The 52-year-old star, who also fronted Audioslave, was found dead in a Detroit hotel room following a Soundgarden concert at the Fox Theatre in the city.
Police said Cornell’s wife had called a family friend and asked him to check on the singer at the MGM Grand Detroit hotel.
Officers said the friend forced open a door and found Cornell in the bathroom.
The musician, who was also a skilled songwriter, had tweeted a picture of the music venue shortly before the sold-out show, writing: “Finally back to Rock City!!!!!”.
His representative described his death on Wednesday night as “sudden and unexpected”, and said his wife and family were in shock.
A preliminary post-mortem examination has been carried out.
Tributes have been pouring in, with Jane’s Addiction and Red Hot Chili Peppers guitarist Dave Navarro tweeting: “SO SO stunned to hear about Chris Cornell! Such a terrible and sad loss! Thinking of his family tonight! RIP”
Aerosmith guitarist Joe Perry tweeted: “Very sad news about Chris Cornell today. A sad loss of a great talent to the world, his friends and family. Rest In Peace.”
Elton John: “Shocked and saddened by the sudden death of Chris Cornell. A great singer, songwriter and the loveliest man.”
Grammy Award-winning Cornell, who formed Soundgarden in 1984, was one of the leading voices of the 1990s grunge movement originating in Seattle.
Among his most famous songs were Soundgarden’s 1994 grunge theme Black Hole Sun, and Hunger Strike – a 1991 hit for another of his rock bands, Temple Of The Dog, where he teamed up with Pearl Jam’s Eddie Vedder.
Cornell was also known for the James Bond theme song You Know My Name from the 2006 movie Casino Royale.
Soundgarden disbanded in 1997, and Cornell pursued a solo career
In 2001, he joined Audioslave which included former Rage Against the Machine members Tom Morello, Brad Wilk and Tim Commerford.
They broke up in 2007 due to tensions in the group and Cornell continued to pursue his solo career.
He reunited with Soundgarden in 2010 and they released a sixth studio album, King Animal, two years later.
Earlier this year he released a new solo single titled The Promise.
Cornell had also been involved in philanthropy and started the Chris and Vicky Cornell Foundation to support children facing poverty and abuse.
Soundgarden’s current tour kicked off in late April and had been due to run until 27 May.
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