The incidents are said to have taken place at the school between 1968 and 1992.
Five men, aged between 69 and 90, have been arrested and charged in connection with alleged, non-recent, abuse incidents at Edinburgh Academy, police have said.
Police Scotland said that a sixth man, aged 74, will also be reported to the procurator fiscal.
The abuse incidents are alleged to have taken place at the school between 1968 and 1992.
Edinburgh Academy previously apologised for historic abuse after it was investigated as part of the Scottish Child Abuse Inquiry.
Nearly 50 witnesses gave evidence to the inquiry, including broadcaster Nicky Campbell who spoke publicly about the abuse he said he had suffered.
Detective Inspector Colin Moffat, of Police Scotland, said: “We would like to thank everyone who has come forward and assisted our inquiries to date.
“While the investigation of child abuse, particularly non-recent offences, can be complex and challenging, anyone who reports this type of crime can be assured that we will listen and we will investigate all reports, no matter when those offences occurred or who committed them.
“If you have suffered abuse, or you know anyone who may have been the victim of child abuse, then please call Police Scotland on 101.”
