The Avon and Somerset Constabularly, based in the English town, today formally identified the victim as 22-year-old Garrett Elsey.
The Edmonton-area man was found dead at a recycling facility in Avonmouth last Thursday.
Police spokesman Wayne Baker says the investigation is continuing with the help of the coroner.
He says a post-mortem has already been conducted.
But he says police have yet to determine how Elsey's body ended up in the facility, adding that will be part of the investigation.
"We have provisional findings but further investigations are taking place in conjunction with the coroner," Baker said.
"These are likely to take some time. But we can confirm that the death is not being treated as suspicious."
The family has requested privacy during the investigation. A family member earlier said that Elsey went to Bristol to study for a master's degree in international security.