In the video, almost identical to those released after three previous murders, a masked IS militant also threatens a hostage he identifies as an American, Peter Kassig.
Both men were volunteers working to bring aid to civilian populations in Syria when they were captured. Henning, 47, was a driver in a humanitarian convoy organized by an Islamic charity.
Kassig, who is still alive at the end of the one-minute 11-second video, is a former US Army soldier who served in Iraq then returned to the Middle East to found a relief organization.
Britain's Prime Minister David Cameron confirmed that the video appeared to be genuine and condemned the murder, saying it "shows just how barbaric and repulsive these terrorists are."
"We will do all we can to hunt down these murderers and bring them to justice."
The video, found online by the SITE private terrorism monitor, opens with a news report about the British parliament's vote last week to authorize air strikes against jihadist targets in Iraq.
Then it cuts to Henning, on his knees against a desert backdrop and wearing an orange prison-style outfit, with a masked militant standing over him wielding a combat knife.
Henning explains to camera that, as a member of the British public, he is being made to pay the price for the parliamentary vote.
Then the militant, who has the same British accent as the killer in a previous IS video of the death of British hostage David Haines, directly addresses Cameron.
"The blood of David Haines was on your hands, Cameron. Alan Henning will also be slaughtered, but his blood is on the hands of the British parliament," he declares, then cuts the hostage's throat.
(Image received from Britain's Foreign and Commonwealth Office on September 15, 2014 shows British aid worker, Alan Henning holding a child in a refugee camp on the Turkish-Syrian border - AFP PHOTO)
After the beheading the video cuts to a similar scene in which the killer introduces a man as Kassig, an aid worker in his twenties who had gone missing after heading to the region.
"Obama, you have started your aerial bombardment in Sham, which keeps on striking our people," the militant says, using the Arabic term for Syria and the Levant.
"So it is only right that we continue to strike the necks of your people."
The video ends with the second hostage apparently unharmed. Previous IS victims have been threatened in this way before appearing around two weeks later in videos of their murders.
'Brutality'
Kassig was interviewed by Western media in 2012 before his disappearance and said that having left the army he felt compelled to return to the Middle East and find ways to help the war injured.
The IS group, a militant army recruited from former Al-Qaeda rebels in Iraq, extremist foreign fighters and radical Syrian anti-government rebels, has seized a large tract of territory in Iraq and Syria.
The extremists have previously released videos also showing the murders of American journalists James Foley and Steven Sotloff.
In Washington, President Barack Obama's top counter-terrorism advisor Lisa Monaco said US officials were trying to confirm the video's authenticity.
"If it in fact proves to be authentic, it is yet another demonstration of the brutality of ISIL and our hearts go out to the British aid worker who we believe is in that video," she said.
The United States and a coalition of Western and Arab allies, now including Britain, are waging an aerial campaign to strike IS targets in Iraq and Syria, hoping to reverse the group's lightning advance.
