The Wayne County Medical Examiner's Office confirmed in a statement the frontman, who also sang for the band Audioslave, had taken his own life.
With his powerful, almost four-octave vocal range, Cornell was one of the leading voices of the 1990s grunge movement with Soundgarden, which emerged as one of the biggest bands out of Seattle's emerging music scene, joining Nirvana, Pearl Jam and Alice in Chains.
The statement said the family would be working with a medical examiner to determine the cause of death and requested privacy.
"The cause of death has been determined as suicide".
Cornell, 52, was found dead in a hotel room at the MGM Grand Detroit after having performed with Soundgarden at the Fox Theatre.
Meanwhile, Jason Aldean, who performed Just Gettin' Started with the late rocker at the 2014 CMT Artists of the Year special, adds, "I only got to work with Chris once, but he was a true rock star".
Soundgarden disbanded in 1997 due to tensions in the band, and Cornell pursued a solo career.
Born and raised in Seattle, Cornell became well involved in the city's underground music scene at a young age, starting in the band The Shemps in the early 80s before eventually forming Soundgarden in 1984.More news: Labour spending plans to create £58bn hole in public finances, claim Tories
The singles "Black Hole Sun" and "Spoonman" off the band's "Superunknown" album, which came out in 1994, earned them two Grammys. "I'm just shocked", he said.
Singer Chris Cornell died as a result of hanging himself, United States officials have confirmed.
He entered rehab in 2002, separating from his first wife, Helen Silver, and forcing Audioslave to back out of its first tour. In 2001, he joined Audioslave, a supergroup that included former Rage Against the Machine members Tom Morello, Brad Wilk and Tim Commerford.
The breakup wasn't anything unusual, Cornell told CNN in 2012.
Cornell has also rolled out five solo albums in 16 years. And then part two of that is, like, accept it when it comes and, you know, believe what people tell me. After splitting in 1997, they reunited in 2010 for their sixth studio album King Animal, with the band having sold more than 10.5 million records in the USA as of 2012 and winning two Grammy awards.
At the time of his death, he was splitting his time between California and Paris, the base for Karayiannis, his second wife, with whom he has a daughter and a son.
Heavy is the Head gave the Zac Brown Band number ones in both the Mainstream Rock and Country Airplay charts in the U.S. It was also the final number one for Cornell. "A great singer, songwriter and the loveliest man".