People magazine said the 52-year-old rocker's remains were cremated Tuesday, with a private funeral held Friday and a public memorial at Hollywood Forever Cemetery later in the day.
Soundgarden guitarist Kim Thayil and drummer Matt Cameron, Audioslave co-founder Tom Morello and actor Josh Brolin offered eulogies, and Linkin Park's Chester Bennington sang "Hallelujah," USA Today reported.
Cornell hanged himself in his hotel room May 18 after performing with his band Soundgarden on May 18. He is survived by his wife Vicky and three children.
The musician's family has said they object to the medical examiner's categorization of his death as a suicide since toxicology reports are not yet complete. His loved ones have said they believe drugs, specifically Ativan, may have played a role in his death.