The man in his early 60's and originally from Louth was found slumped on a bench on Kenyon Street at around 7.30 yesterday evening.
Emergency services were called but he was pronounced dead a short time later and his body taken to Limerick University Hospital for a post-mortem.
Gardaí have ruled out foul play and the man's family have been contacted.
He had been living in Nenagh for several weeks with people describing him as a gentle giant and local business people had been providing him with food.
In a statment this evening GSOC said they were contacted as a routine procedure as officers in Tipperary had met the man earlier in the day when they found him lying on the ground Ballygraigue Road, Nenagh and brought him to the Homeless Shelter on Kenyon Street.
GSOC officers travelled to Nenagh earlier today as part of their investigation which must be conducted when there has been death or serious harm to a person and there has been contact with a garda prior to this.
Locals expressed their shock and upset at the man's sudden death while students undergoing exams at the nearby Secondary School said they used to regularly speak with him
