John Young was found to have targeted pupils while employed as a PE teacher at the independent school in the capital between 1966 and 1993.
The 91-year-old was deemed medically unfit to be criminally tried or to appear in court.
However, following an Examination of Facts at Edinburgh Sheriff Court, the Sheriff ruled that Young had repeatedly abused children, with 26 charges found to be established
Prosecutor Fiona Kirkby, of the Crown Office and Procurator Fiscal Service (COPFS) said:
“The Crown Office and Procurator Fiscal Service consistently and successfully strives to secure justice for those affected by non-recent abuse.
“John Young systematically abused young boys, over a period of 27 years, while holding a significant position of trust as their teacher at the Edinburgh Academy.
“He had a duty of care to nurture and support these children but instead intentionally exploited his power to violate and humiliate them.
“This Examination of Facts is a public airing of the facts and an acknowledgement that what happened to these children in the past was criminal. It should never have occurred.
“It is now a matter of public record that Young committed offences including lewd and libidinous behaviour, indecent assault and cruel and unnatural treatment.
“The court’s finding today also sends a clear message to abusers: no matter who you are, when the abuse happened or how long after the event it is reported, there will be a robust response from prosecutors.”
Evidence was heard from 24 former pupils – and a further three witnesses - during the hearing.
Some of the victims detailed how the teacher would use violence to punish pupils for perceived bad behaviour, including punching them or hitting them with a cricket bat, megaphone or wooden wedge.
Many told how they continue to be traumatised and struggle to trust figures of authority because of the abuse they suffered.
The court had previously determined that the accused was not fit to stand trial and ordered an Examination of Facts, where the Procurator Fiscal depute and the defence led evidence, which was tested before a sheriff.
Procurator Fiscal Fiona Kirkby added: “Sexual abuse and the use of force upon children is a crime.
“To any victim of such offending, we urge you to report it when you feel ready and able to do so. Be assured you will be listened to and supported. We remain committed to investigating and pursuing those culpable to seek conclusions.”