Paramedics and firefighterswere called to the scene at the Duke and Duchess of Cambridge's Palace early this morning, but the man, was pronounced dead on the scene.
According to the'Evening Standard',officers stationed at the royal household were the first to respond to the incident, involving a man in his forties.
A statement from Scotland Yard said: "Officers in Westminster were called by a central London hospital at 12:06am on Tuesday, February 9 after a man in their care had failed to return.
The Metropolitan Police had been alerted after the man walked out of a central London hospital after presenting with mental health problems.
The incident is not being treated as suspicious or as terrorist related, and the man's actions are not thought to have been a form of protest.