The man’s body was found in the Slateford area shortly after 8am this morning.
It is understood the man in his mid 30s tried to scale a fence next to the track but came too close to the overhead pylons.
A train driver raised the alarm after spotting the body next to the line.
A spokesman for British Transport Police said enquiries were at an early stage but the incident is being treated as non-suspicious.
“Our officers were called to the line near Haymarket station at 8.45am on Tuesday, 22 July, after reports of a man’s body on the line.
“Colleagues from Scottish Ambulance Service also attended, but the man was pronounced dead at the scene.
“We are now working to formally identify the deceased and will subsequently inform his family.
“The incident is not currently being treated as suspicious and a full report has been submitted to the local Procurator Fiscal.”
The incident is causing disruption to services between Edinburgh and Glasgow Central via Shotts and is expected to do so until at least 11am.
Customers with valid tickets from Glasgow Central to Edinburgh can use tickets to travel on alternative routes from Glasgow Queen Street to Edinburgh via Falkirk High and Airdrie.
Those travelling to or from Livingston South station with valid tickets can also use Livingston North as an alternative.
Train operator Scotrail urged customers to check before travel by visiting its website.