The 52-year-old star hanged himself, according to the Wayne County medical examiner's office, but results of a full post-mortem exam and toxicology tests are awaited.
Cornell's ashes were buried at the Hollywood Forever Cemetery in Los Angeles on Friday afternoon, local time.
Also at the private ceremony were Jimmy Page, James Franco, Dave Navarro, Krist Novoselic. Nile Rodgers, Billy Idol and Tom Morello.
Morello, Cornell's bandmate in Audioslave, said during a eulogy: "Chris was as melodic as The Beatles, as rocking as Sabbath and as haunting as Edgar Allan Poe".
Other eulogies came from actor Josh Brolin, Soundgarden bandmates Kim Thayil and Matt Cameron.
Linkin Park's Chester Bennington performed Leonard Cohen's Hallelujah.
A public memorial was held afterwards.
Father-of-three Cornell was cremated in a private ceremony on Tuesday, reportedly attended by four people, including his widow Vicky.
In a tribute posted on Billboard.com, she wrote a letter to her husband of more than a decade, saying: "I'm sorry you were alone, and I know that was not you, my sweet Christopher.
"Your children know that too, so you can rest in peace."
She said she was "broken" but vowed to "stand up" for her late husband and take care of their children.
Mrs Cornell has previously indicated that the star might have taken a higher dose of an anti-anxiety drug than he was prescribed.
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