Two other Isis (Islamic State) fighters were killed in the attack, in the Syrian city of Raqqa, on August 21. One of them, Ruhul Amin, 26, was also a British citizen, Cameron said. He said a third Briton, Junaid Hussain, 21, was killed by a separate US air strike.
Khan, 21, was targeted after it emerged he was leading a plot to attack the VJ Day commemoration services in London last month, government sources said. The Queen, the Prince of Wales, and the Prime Minister were at the service in central London. Yet the strike took place six days later. Cameron claimed that Khan would never "desist from his desire to murder us at home".
The strike was condemned by Labour MPs, human rights organisations and a number of senior Tories.
The disclosure comes days before Labour is expected to elect Jeremy Corbyn as leader. He has repeatedly said he would not back military intervention in Syria. The announcement of the strike comes amid speculation that Cameron is preparing the ground for a military intervention in Syria.
The drone strike was approved by the Prime Minister "months ago" at a meeting of the National Security Council (NSC), sources said. The request to authorise the attack came last month. Michael Fallon, the Defence Secretary, gave the go-ahead at a meeting of the NSC on the Prime Minister's behalf, Downing St said.
Defence sources said that British spy planes were used to locate Khan before the fatal drone attack was authorised.
A Rivet Joint plane packed with sensitive electronic eavesdropping intelligence equipment has been flying over Syria from Cyprus since October.
GCHQ's main effort this northern summer has been to sift and analyse traffic from Raqqa, the headquarters of Isis, and Khan's position is understood to have been given away after his communications were intercepted.
Reaper drones
• Unmanned reaper drones are used by the RAF for surveillance and air strikes, and have been deployed against Isis since the end of 2014 after Parliament authorised military action
• Max speed: 466km/h
• Altitude: 15,240m
• Weapons: Hellfire missiles and GBU-12 225kg laser guided bombs
• Length: 10.97m
• First used by Britain: 2007