Nigel Wilson from Nottingham flew the unmanned aircraft over Anfield stadium during a Liverpool Champions League match last September, during match days at Arsenal's Emirates Stadium and Manchester City's Etihad Stadium.
He also flew the drone over the Houses of Parliament, Buckingham Palace, the Shard and HMS Belfast.
He pleaded guilty to seven offences contrary to the Air Navigation Order and was fined £1,800. He was also ordered to pay £600 in costs and banned from purchasing, owning or flying any drones for the next two years.
The Metropolitan Police arrested Wilson last July as part of a joint investigation with the Civil Aviation Authority (CAA).
Chief inspector Nick Aldworth, the Met's leading officer on the misuse of drones, said: "As drones become more widely available, it's important that anyone using this type of small aircraft understands that there are strict regulations on how and where they can be flown and that police, in partnership with the CAA, will look to prosecute anyone who does not follow these rules.
"Flying drones over congested areas or buildings can pose great risks to public safety and security and Wilson pit many people in real danger. Today's outcome should serve as a warning to anyone thinking of doing similar that they could end up in court if they ignore these regulations."