The incident was not being treated as suspicious or related to terrorism, they added.
Police said they had been alerted just after midnight by officials from a central London hospital to say a man in their care had failed to return.
Man battles for life after attempted self-immolation
Three hours later, officers were called to a site near the locked parks of the palace, located in Kensington Gardens in central London, after reports of a man acting suspiciously.
When they arrived they found the man, in his 40s, ablaze. He was declared dead not long afterwards.
Sexual assault: Health worker threatens self-immolation if justice is not served
Kensington Palace is the official London residence of William although he, Kate and their two children, George and Charlotte, spend most of their time at their country mansion in Norfolk, eastern England, close to where the prince works as an air ambulance helicopter pilot.
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