Presley Gerber's body has been released after authorities finished their autopsy ... TMZ has learned.

Online records indicate the body has been let go ... though it doesn't say who is currently in custody of it. His cause of death is still "deferred" for now.

As you know ... Presley died on Sunday at a Los Angeles-area rehab facility. Our sources say his death appeared to be an overdose.

We're told Presley appeared intoxicated when arriving to the facility on Saturday ... and sources with direct knowledge told us a doctor had prescribed Presley ketamine -- a move which infuriated close friends and family who knew he had an issue with the substance.

Authorities immediately ran an autopsy ... and we knew it was completed Monday -- so it makes sense that his family or friends can now pick up his body.

Presley had been dealing with addiction for some time, and even attempted to use the controversial substance ibogaine to free him from it.