Staley co-founded Alice in Chains
The King County Medical Examiner's office, in the United States, ruled out the possibility of suicide or murder as causes of death.
Staley, 34, was found dead in his Seattle home last month surrounded by drug paraphernalia.
The coroner's report put the cause of death as "acute intoxication of combined effects" of heroin and cocaine.
Staley co-founded Alice in Chains in 1987, wrote most of the band's songs with guitarist Jerry Cantrell and sometimes alluded to his battle with drug addiction in his lyrics.
The band signed with Columbia Records in 1989 and worked constantly over the next seven years, recording six albums and touring the world.
Rehabilitation
Along with Nirvana, Pearl Jam and other Seattle bands, the band exemplified the "grunge" sound of the city.
The band played its last concerts together in 1996, after which Staley went into rehabilitation for heroin use.
He once told Rolling Stone magazine that lyrics about heroin use came from his own experience.
"They worked for me for years, and now they're turning against me - and now I'm walking through hell, and this sucks," he said in 1996.
But he had maintained he would never think of committing suicide.
"I'm scared of death, especially death by my own hand," he said.
"At the end of the day or at the end of the party, when everyone goes home, you're stuck with yourself."