The body of Jonathan Scotland, 33, from Glasgow was found outside Blythswood Court by a member of the public on Wednesday.
The incident sparked an alert as police cordoned off the area in Cadzow street.
An incident tent was set up in the street below the public walkway leading from Blythswood Court’s Davaar block to the other two high rise buildings in the housing complex.
Several uniformed officers as well as plain clothed officers scouered the scene carrying out inquiries.
As well as Blythswood Court, the busy area is home to commercial businesses.
At the time, residents of the housing complex spoke of their shock.
A Police Scotland spokeswoman said: “Mr Scotland’s death is being treated as suspicious and enquiries are continuing.
“A report will be submitted to the Procurator Fiscal.”