Officers were called to the A720 between the Sheriffhall and Gilmerton junctions at around 8.20am on Thursday after drivers raised the alarm.
It is understood the road is likely to remain closed in both directions for some time.
Diversions are in place and motorists are being urged to avoid the area.
Detectives are at the scene along with road policing officers.
Police said the identity of the man, whose death is being treated as unexplained, would not be released until his next of kin had been informed.
A Police Scotland spokesperson said: “We are currently in attendance on the A720 following the discovery of a man’s body on the central reservation.
“The incident was reported to police at around 8.20am on Thursday, January 17.
“Inquiries into the full circumstances are ongoing, and the death is being treated as unexplained. A report will be sent to the Procurator Fiscal.
“Closures are currently in place on the Edinburgh City Bypass in both directions. The public is thanked for their patience at this time.”
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