British Transport Police said officers were called to the line in Horsham at 11.07am following reports of a casualty on the tracks.
Southern Rail added that all lines are blocked between Horsham and Arundel after a person was ‘hit by a train’.
A police spokesman added: “Paramedics also attended however sadly a person was pronounced dead at the scene. Officers are now working to identify the person and inform their family.”
The incident is not being treated as suspicious and a file will be prepared for the coroner, said police.
A Southern Rail spokesman added: “Services between London Victoria and Bognor Regis / Portsmouth Harbour / Southampton Central will be cancelled by this incident.
“If you need to travel to Barnham / Bognor Regis from London, we advise you to travel to Brighton and change trains there.
“South Western Railway will accept tickets between Portsmouth / Southampton and London Waterloo via Guildford.”
Those services will have a reduced capacity, as South Western has been affected by a landslip on their network, Southern said.
The spokesman added: “If you require stations between Horsham and Arundel, we have requested rail replacement buses to operate and we will provide a further update once the buses are in place.
“If you have not yet started your journey then please delay travelling until later as we currently cannot run trains between Horsham and Arundel.”
Southern said anyone using the following stations should delay their journey:
Disruption is expected until around 2pm today.