The Detroit Free Press reported that Detroit police social media manager Dontae Freeman said Cornell was found dead in a hotel room at the MGM Grand Detroit hotel with "a band around his neck".
Cornell was pronounced dead in the room.
"We are saddened to hear of the loss of Soundgarden's Chris Cornell", the venue tweeted.
Cornell's family was in shock after his "sudden and unexpected" death, according to a statement released by his representative Brian Bumbery. A medical examiner has determined that the Soundgarden singer committed suicide by hanging.
"They would like to thank fans for their continuous love and loyalty and ask that their privacy be respected at this time", the statement said.
The 52-year-old Cornell was on tour and performed Wednesday night in Detroit with Soundgarden.
YouTube user "Uncle Sam" has uploaded a series of clips showing what is believed to be his last song - "Slaves & Bulldozers" merged with a Led Zeppelin's In My Time of Dying. In 1984, he formed the band Soundgarden, which was influential in the grunge-rock movement of the early 1990s.More news: Watch Cristiano Ronaldo score record-breaking goals in La Liga — Real Madrid
Festival organizers announced the cancellation late Thursday morning, citing the sudden death of Soundgarden lead singer Chris Cornell. Singer Layne Staley and bassist Mike Starr of Alice in Chains each died of drug-related causes, in 2002 and 2011, respectively. "They're all young and these guys all had limitless potential in their lives in front of them".
Nirvana thought Pearl Jam were, in the words of J D Salinger, "a bunch of phonies" who had nothing to do with them.
With his flowing curly hair and often bare chest, Cornell showed off his vocal skills on Soundgarden hits such as "Black Hole Sun", set to dissonant minor chord progressions on guitar.
Soundgarden got back together after 13 years off the road, and one of their first stops after reuniting was a headlining slot at 2011's Voodoo Music Experience.
"It's hard not to be a little bitter about it", Cornell said.
Soundgarden returned to the stage in 2010 for festival performances and had recently started touring again. "It's what we missed when we weren't a band", Cornell had posted on Facebook on Tuesday. Thinking of his family tonight!
What we can absolutely do, though, is celebrate what Chris Cornell, and those we have lost before him, have left behind. "But, like I said before, but his wife is disputing that, so only time will tell".
CNN Wire and the CNN Video Affiliate Network is an online syndication service providing text and video versions of CNN's award-winning news coverage. The Detroit News cited Freeman in a similar report.