The body of Craig Bruce, 37, was found on the central reservation of the A720 between the Sheriffhall Roundabout and the Gilmerton Junction at around 8.20am on Thursday.
Police are investigating the circumstances of his death.
Officers believe a white and black Fiat Ducato van, travelling westwards from Sheriffhall Roundabout, was involved in a collision and that this van was then overtaken by two HGVs before the Straiton junction.
They are urging the drivers of the two HGVs, or anyone who saw a white and black Fiat Ducato van travelling in the area at around 1am, to contact police.
Sergeant Ross Drummond from Police Scotland’s Road Policing Unit said: “Our investigation into what happened remains ongoing, and our thoughts continue to be with Mr Bruce’s family and friends.
“We’re particularly eager to trace two lorry drivers who were travelling westbound between Sheriffhall and the Straiton junction at around 1am, and who may be witnesses in our inquiries.
“I’d again ask anyone who was travelling on the city bypass overnight on Wednesday into Thursday morning, and who may have information or dashcam footage that can assist our investigation, to get in touch and provide this at their earliest opportunity.”
The road was closed in both directions for around eight hours while police carried out investigations at the scene.
Mr Bruce was from Bilston in Midlothian.