The 44-year-old aid worker David Haines was seized in Syria in 2013 and was being held by IS militants who have already killed two US journalists.
A new two-minute-27-second video titled "A Message to the Allies of America" blames Cameron for joining forces with the US, which has said it is at "war" with the jihadists and launched air strikes against them in Iraq. The latest video showing his killing also includes a threat to kill a second British hostage. Cameron vowed to do everything possible to find the killers.
"It is an act of pure evil. My heart goes out to the family of David Haines who have shown extraordinary courage and fortitude throughout this ordeal," he said.
"We will do everything in our power to hunt down these murderers and ensure they face justice, however long it takes," he added.
The UK Foreign Office is working to verify the video, which was released last night. It begins with a clip of Cameron and then features a man who appears to be Haines dressed in orange overalls, kneeling in front of a masked man holding a knife.
The victim says, "My name is David Cawthorne Haines. I would like to declare that I hold you, David Cameron, entirely responsible for my execution".
He says Cameron had entered into a coalition with the US against the IS "just as your predecessor Tony Blair did".
"Unfortunately it is we the British public that in the end will pay the price for our parliament's selfish decisions," he said.
The militant, who appears to have a British accent, is then recorded as saying "This British man has to pay the price for your promise, Cameron, to arm the Peshmerga against the Islamic State".
Haines's family said he would be "missed terribly". "David was most alive and enthusiastic in his humanitarian roles.
His joy and anticipation for the work he went to do in Syria is for myself and family the most important element of this whole sad affair," his brother Mike Haines said in a statement released through the Foreign Office.
US President Barack Obama also condemned the "barbaric murder" of Haines which in recent weeks has killed two American journalists James Foley and Steven Sotloff in the same manner.
"The United States strongly condemns the barbaric murder of UK citizen David Haines by the terrorist group ISIL. Our hearts go out to the family of Mr Haines and to the people of the United Kingdom," Obama said in a statement.
"The United States stands shoulder to shoulder tonight with our close friend and ally in grief and resolve," said the president after the IS posted the video on social media showing the killing of the British citizen.
"We will work with the United Kingdom and a broad coalition of nations from the region and around the world to bring the perpetrators of this outrageous act to justice, and to degrade and destroy this threat to the people of our countries, the region and the world," Obama said.
Australian Prime Minister Tony Abbott said Haines's murder was "further demonstration that this particular terrorist group does not just do evil, but exults in doing evil".
The French presidency said in statement that, "The heinous murder of David Haines shows once again how the international community must mobilise against the IS".
The IS, which seeks to establish an Islamic Caliphate across the Middle East, controls a large swathe of territory extending from the north and east of Syria, to almost all the mainly Sunni parts of Iraq.
The group controls a population of around 5 or 6 million people, including Iraq's second largest city, Mosul. In northern Iraq, the Kurdish Peshmerga force, helped by US air strikes, are slowly regaining the ground they lost to the IS when it suddenly turned on them last month.