The incident, above an estate agents, happened in High Street just after midnight.
Detective Chief Inspector Danny Long, from West Midlands Police said the man was believed to have lived in the one of the two flats on the second floor of the building.
"At the moment we can't tell what time this person died or where he was in the building when the roof collapsed.
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"Obviously the roof went through not just the first floor but through to the ground floor.
"We don't know how far he fell. We can't say at this stage."
The weight of the collapsed roof caused the floors below to give way.
Two men made their own way out of the building and firefighters rescued two other men.
A fireservice spokesperson said: "The roof collapsed inwards, which caused the floors below to pancake downwards towards the ground floor."
He described the incident as a "catastrophic failure".
The men were taken to hospital and suffered minor injuries. The cause of the collapse is unknown.
(CD/JM)
