Ian Mitchell, 63, was found dead at his address in Lockharton Avenue in the Craiglockhart area on Thursday.
Police said there were no suspicious circumstances surrounding his death, and a report will be sent to the procurator fiscal. Mr Mitchell worked as a waiter in La Rusticana Italian restaurant in Hanover Street for 11 years.
A police spokesman said: “He is believed to have a brother and sister in Glasgow.”