The incident happened on Saturday, March 14 as officers attended reports of a casualty on the tracks near Royal Wootton Bassett just after 2.10pm.
Despite the efforts of the emergency services, a person was pronounced dead at the scene.
Police said the incident was not thought to be suspicious and added the case will go to the coroner.
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A spokesperson for British Transport Police said: “Officers were called to a report of a casualty on the tracks just after 2.10pm on Saturday (14 March) near Royal Wootton Bassett.
“Officers and paramedics attended and sadly a person was pronounced deceased. The incident is not thought to be suspicious and a file will be prepared for the coroner.”
The incident caused cancellations of a number of trains between Swindon and Bristol Temple Meads throughout the afternoon and evening and drew a significant emergency response.
A spokesperson for Dorset and Wiltshire Fire Service said crews from Royal Wootton Bassett and Westlea were called to the road Royal Wootton Bassett at 2.24pm to assist with a multi-agency incident.
The added: “No action was carried out by firefighters – our stop was in at 3.19pm and incident handed over to the police.”
A spokesperson for the South Western Ambulance Service NHS Foundation Trust (SWASFT) said: “We were called at 14:18hrs on Saturday 14 March to an incident near Royal Wootton Bassett. We sent a double-crewed land ambulance, a critical care car a rapid response vehicle and a hazardous area response team to the scene.”
