Emergency services were called to the line near Colwich Junction, near Rugeley, at around 7.45am on Friday. The person was pronounced dead at the scene.
Staffordshire Police say it is believed to be the body of the missing 51-year-old, who was last seen in Great Haywood on September 28. Formal identification is due to take place and his family are being supported by officers.
A spokesman for the force said: "Officers from Staffordshire Police have called off the search for missing person Robert Thornton, who was last seen in Great Haywood, near Stafford, on Monday, September 28.
"Sadly, the body of a man, believed to be 51-year-old Robert, was found near to the railway line in Colwich, near Stafford, at this morning.
"Formal identification is due to take place. Robert's family are being supported by specially-trained officers and have asked for privacy at this difficult time."
A spokesman for British Transport Police said: "Officers were called to the line near Colwich Junction at 7.44am on Friday, October 16, following reports of a casualty on the tracks.
"Paramedics also attended but a person has sadly been pronounced dead at the scene.
"Officers are now working to identify the person and establish the full circumstances behind their death."
A West Midlands Ambulance Service spokesman added: "We were called to reports of a patient near to the railway line by Colwich Junction at 7.49am on Friday morning. One ambulance, a paramedic officer and our Hazardous Area Response Team attended the scene.
"On arrival we discovered one patient, but sadly it quickly became apparent nothing could be done to save them and they were confirmed dead at the scene."
Colwich Junction lies between Rugeley and Stafford.