The body of the man has been identified as 33-year-old Barry McLachlan from Glasgow.
Officers received a report around 2am on Saturday, July 3 that a man had been found injured in a common close on Knapdale Street.
Emergency services attended and he was pronounced dead at the scene.
The police are treating the incident as murder and a 26-year old has been arrested in connection with the death.
He is due to appear at Glasgow Sheriff Court on Tuesday, 6 July, 2021.
Detective Inspector Peter Crombie, senior investigating officer, said : “Our thoughts are very much with the family and friends of Barry and officers are providing support at this difficult time for them.
“I would like to thank members of the local community for their assistance in this enquiry and to reassure them there is no threat to the wider public.”