Police are treating the death of 33-year-old Jonathan Scotland, from Glasgow, as suspicious.
Officers were called to Blythswood Court in the city centre at about 1.30am yesterday.
The surrounding area was sealed off following the discovery of the body.
Police Scotland said the man had died after falling from the eighth floor of the block.
“Mr Scotland’s death is being treated as suspicious and inquiries are continuing,” the force said in a statement.
A report will be sent to the procurator fiscal.