Emergency services were called to station shortly after 9.30am this morning (Tuesday).
A person, understood to be aged 20, was pronounced dead after paramedics tried to save them.
Trains have been cancelled causing major delays for commuters.
The station, including the restaurant, has been cordoned off while investigations are carried out.
A British Transport Police spokesman said: “Police and paramedics from the Scottish Ambulance Service attended, despite their best efforts the person could not be saved.
“Officers remain on scene and are making enquiries to establish how the person came to fall.
“Likewise, they are working to identify the person and inform their family.”
A Scottish Ambulance Service spokesman added: “We received a call at 9.31am to attend an incident at Bearsden train station.
“We dispatched two ambulances, an advanced paramedic unit, a paramedic response unit and our trauma team to the scene.”
Strathkelvin and Bearsden MSP Rona Mackay said: “My thoughts are with the family of this man at this heartbreaking time. It is such a terrible tragedy – my heart goes out to them.”