The rock singer had earlier played a concert in the city's Fox Theatre that evening.
Tributes from fellow muscians poured in on Thursday. Elton John said he was "shocked and saddened". He said Cornell was "a great singer, songwriter and the loveliest man".
Led Zeppelin guitarist Jimmy Page said: "RIP Chris Cornell. Incredibly Talented. Incredibly Young. Incredibly Missed."
Remembering Chris Cornell (1964 - 2017)
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Cornell was one of the most lauded and respected contemporary lead singers in rock music, thanks to his charismatic energy onstage and wide vocal range.
He was a leader of the grunge movement with Seattle-based Soundgarden - with whom he gained critical and commercial acclaim - but also found success outside the band with other projects, including Audioslave, Temple of the Dog as well as with solo albums.
* For confidential support on mental health call Samaritans free from any phone, at any time, on 116 123 (UK & RoI) or email jo@samaritans.org.
Additional reporting by AP
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