Separately, Turkish officials in Istanbul say they have detained a British man, believed to be Aine Lesley Davis, an alleged accomplice to "Jihadi John". Aine Davis is believed to have been guarding foreign prisoners in Syria.
'Strike at IS heart'
Speaking outside Downing Street, Mr Cameron said it was not certain whether the strike was successful, but the UK had been working with the US "literally around the clock" to track Emwazi down.
He said any successful attack would have been "a strike at the heart" of Islamic State (IS), and would demonstrate to those who would harm Britain that "we have a long reach, we have unwavering determination and we never forget about our citizens".
Three drones - one British and two American - were involved in the strike. One of the American drones hit the militants' car.
Emwazi appeared in beheading videos of victims including British aid worker David Haines and taxi driver Alan Henning.
Mr Haines's daughter Bethany said she felt an "instant sense of relief" upon hearing reports of Emwazi's possible death, "knowing he wouldn't appear in anymore horrific videos."
"He was only a pawn in Isis's stupid game, but knowing it's over, that he's finally dead, still hasn't sunk in," she said in a statement.
"As much as I wanted him dead I also wanted answers as to why he did it, why my dad, how did it make a difference?"
The Henning family were informed on Thursday night by a government contact that the strike had taken place, the BBC understands.
Stuart Henning, Mr Henning's nephew, wrote on Twitter: "Mixed feelings today wanted the coward behind the mask to suffer the way Alan and his friends did but also glad it's been destroyed."
Labour leader Jeremy Corbyn said it appeared Emwazi had been "held to account for his callous and brutal crimes".
"However, it would have been far better for us all if he had been held to account in a court of law," he said.
On Twitter, a group called Raqqa is Being Slaughtered Silently posted a map claiming to show the location of the drone strike.
It added: "The good thing is #JihadiJohn got killed near Clock tower where #ISIS Execute people."
Analysis: Frank Gardner, BBC security correspondent
As the militant who sadistically murdered Western aid workers and journalists on camera, Mohammed Emwazi became a top target for US and British intelligence agencies, even though he is thought to have played no military role within Islamic State.
After his identity was revealed in February, Emwazi largely stayed out of sight, taking particular care not to leave a digital trail to his whereabouts.
But GCHQ, the UK government's communications headquarters, has expended enormous efforts to intercept and decipher any encrypted messages that might reveal his location or those of his associates.
Emwazi is believed to have travelled to Syria in 2013 and later joined IS militants.
He first appeared in a video in August last year, when footage was posted online showing the murder of US journalist James Foley.
Civil war erupted in Syria four years ago, and now President Bashar al-Assad's government, IS, an array of Syrian rebels and Kurdish fighters all hold territory. Millions have been displaced and more than 250,000 people killed as a result of the fighting.