The man was found dead in shrubs outside a high-rise flats building in the Heath Town area of the city on Tuesday.
Police and paramedics were called to Hawthorn House in Clover Ley at around 5.30pm but the 44-year-old man was pronounced dead at the scene.
It is believed the man, who lived in the tower block, may have been there for more than 24 hours before his body was discovered.
The cause of death is currently being treated as unexplained and a post mortem examination is taking place on Wednesday to shed light on what happened.
A 40-year-old man, who is known to the deceased, has been arrested and remains in custody while officers conduct further enquiries.
West Midlands Police has not said what he has been arrested on suspicion of.
Meanwhile neighbours have been left saddened and shocked at hearing of a death so close to their home.
A spokesman for the force said: "The cause of death is currently being treated as unexplained and a post mortem examination is due to take place.
"We’ve arrested a 40-year-old man, who is known to the deceased, and he remains in custody while we conduct further enquiries."
A West Midlands Ambulance Service spokeswoman said: “We were called at 5.36pm to reports of an incident at an address on Clover Ley, Wolverhampton. We sent one ambulance, a paramedic officer and the Midlands Air Ambulance Critical Care Car to the scene.
"On arrival, we discovered one patient, a man, it immediately became clear that nothing more could be done to save him and he was confirmed deceased at the scene.”
Police have urged any witnesses or anyone who was near Hawthorne House since late morning on Tuesday and who may have seen anything to contact them.
Call the force on 101 or message on Live Chat via their website quoting log 3345 from 9/11.