Cornell, 52, was found dead in his hotel's bathroom an hour after wrapping up his concert with the band in Detroit's Fox Theatre, reported The Telegraph.
His representative, Brian Bumbery called the musician's death "sudden and unexpected" and said in a statement that the family would be "working closely with the medical examiner to determine the cause".
The statement also read Cornell's wife and family are in a shock and they have asked for privacy.
"The cause of death has been determined as suicide by hanging. A full autopsy report has not yet been completed," the Medical Examiner's Office said in a statement after conducting an initial autopsy.
The singer was reported to be in good spirits at his last show and talked about "the next place we play".
Cornell also sang the theme song, "You Know My Name" of the 2007 James Bond movie "Casino Royale".