Mr Kelly was originally found dead in unexplained circumstances near his home in Buncrana, Co Donegal, sparking a major Garda inquiry.
A married father-of-two, Mr Kelly’s body was found in a laneway behind his home at Knockalla Drive on Friday evening.
Originally from Derry’s Top of the Hill area, he had been living in Buncrana for more than 20 years.
The area around Mr Kelly’s home was sealed off overnight on Friday and a post mortem examination was carried out on Saturday.
A Garda spokesman said: “The focus of An Garda Síochána, at this time, is assisting the coroner in the preparation of a file for an inquest on a personal tragedy.”
Mr Kelly, who was in his fifties, had worked as caretaker at Buncrana’s St Oran’s National School.
A candle-lit prayer vigil in his memory was held in the grounds of the school on Saturday evening.
Buncrana parish priest, Fr Francis Bradley led the vigil at which Derry’s unofficial anthem The Town I Loved So Well was sung.
In a post on social media, the school’s parents’ association paid tribute to the late Mr Kelly who was known for his community work in the town.
The association said: “He cared for our building but more importantly, he cared for each and everyone of us, from the youngest child to the oldest adult.”
Mr Kelly’s funeral will take place from his home tomorrow to St Mary’s Oratory in Buncrana for Requiem Mass at 10am.
He will be laid to rest at St Mary’s cemetery, Cockhill.