Madeley took to Twitter when he spotted the device above the house he shares in Cornwall, with his wife, 67-year-old fellow presenter Judy Finnigan.
The star, 59, said he chased the drone user and published his van registration number on the social media site.
Madeley said “minutes after” his tweet the man reported himself to the police.
Devon and Cornwall Police confirmed they were investigating whether a drone had been used legally.
Madeley said the man “called himself in to police with babbled excuses and apologies” following the incident in Talland Bay, near Looe, at 14:00 BST on Tuesday.
A spokesman for Devon and Cornwall Police said: “Police are looking into the use of the drone and if it was being used in accordance with the law.”
Drones fitted with cameras must not be flown within 50m (164ft) of people, vehicles, buildings or structures, according to the Civil Aviation Authority’s code.
Dr. Hans Mumm