The man, aged 44, was found dead in bushes near his home in the Heath Town area of the city on Tuesday.
His death was initially treated as unexplained and a 40-year-old man was arrested on suspicion of murder.
However police have now confirmed they are not treating the death as suspicious and the suspect has been released.
The body was found in bushes near Hawthorn House in Clover Ley at around 5.30pm on Tuesday and may have been there for more than 24 hours before being discovered, police said.
A statement from West Midlands Police said: "The death is not being treated as suspicious and will be referred to the coroner.
"Our thoughts are with the man's family and friends at this sad time."