Officers were called to the scene just west of Haymarket, Edinburgh, after the man's body was discovered this morning at about 9am.
It is thought the man, whose death is not being treated as suspicious, may have tried to scale a fence near overhead pylons.
The line between Edinburgh and Glasgow Central was closed while the incident was dealt with.
A British Transport Police statement said: "Our officers were called to the line near Haymarket station at 8.45am on Tuesday 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."
Scotrail confirmed on Twitter that service on the line had resumed.