He did not give further details but The Daily Telegraph newspaper, quoting unnamed government sources, said Khan was leading a plot to attack VJ Day commemoration services in London attended by Queen Elizabeth II and Cameron in August.
"Reyaad Khan was killed in a precision air strike carried out on August 21 by an RAF remotely piloted aircraft while he was travelling in a vehicle in the area of Raqqah," Cameron told parliament.
Two other Islamic State jihadists, including Briton Ruhul Amin, also died and no civilians were harmed, the prime minister said. The strike was "entirely lawful," he added.
But Amnesty International UK said Britain had joined the US in conducting "summary executions from the air".
"If we allow this to become the norm, we could have countries all over the world conducting aerial execution of perceived enemies on the basis of secret, unchallengeable evidence," its director Kate Allen said.
Kat Craig of human rights group Reprive added: "Make no mistake -- what we are seeing is the failed US model of secret strikes being copied wholesale by the British government."
- 'Come back before it's too late' -
Cameron argued that the move was necessary because "there was a terrorist directing murder on our streets and no other means to stop them".
"Is this the first time in modern times that a British asset has been used to conduct a strike in a country where we are not involved in a war? The answer to that is yes," he added.
Britain used drone strikes during the war in Afghanistan, and is also using them against IS militants in Iraq after joining in the US-led international coalition launched last year.
Khan, from Cardiff, Wales, went by the nom-de-guerre Abu Dujana Britani. He had written on Twitter how he was being prepared to become a martyr and boasted of executing prisoners.
He left for Syria in 2013 with medical student Nasser Muthana, prompting a desperate plea for his return from his mother, Rukia.
"Please come back before it is too late. You are my only one son," she said.
Posing with Kalashnikovs, Khan and 26-year-old Amin appeared in an IS recruitment video in 2014 after travelling to Syria.
A third Briton, Junaid Hussain, a computer hacker described as a key IS operative, also died in a separate US airstrike, Cameron confirmed.
- Momentum for further action? -
The prime minister said that he supported Britain extending its anti-IS bombing campaign to Syria as well as Iraq.
Cameron has been expected to wait until the main opposition Labour party announces its new leader on Saturday before deciding whether to call a vote on extending air strikes to Syria.
The issue is highly sensitive politically -- he was defeated on taking military action in Syria in 2013 in one of the most damaging foreign policy blows to his previous coalition government.
Michael Clarke, director general of defence think-tank the Royal United Services Institute (RUSI), said the government "looks as if it has decided to create a momentum to action that might be unstoppable".
"The point is not so much that this man was British, but that he was targeted in an area that the UK does not currently regard, legally, as an operational theatre of war for UK forces," he added.
Jeremy Corbyn, the favourite to win the Labour leadership, repeated his opposition to air strikes on Monday.
"My view is that it would create more problems than it would solve," he said.