A militant who appears in the footage says his murder is in retaliation for his country’s continued air strikes in Iraq.
Mr Sotloff, 31, is the second American journalist to be killed by IS terrorists, with his reported death coming just two weeks after James Foley, 40, was executed in a video under similar circumstances.
In the latest video, entitled A Second Message to America, Mr Sotloff appears in an orange jumpsuit against the backdrop of a desert landscape before he is beheaded.
There were reports last night that the masked executioner appeared to be the same man who killed Mr Foley, a man known as “Jihadi John” who is believed to come from London.
In the IS video, he looks at the camera and says: “I’m back, Obama, and I’m back because of your arrogant foreign policy towards the Islamic State despite our serious warnings.
“So just as your missiles continue to strike our people, our knife will continue to strike the necks of your people.”
The executioner points his knife menacingly at the camera as he speaks. At the end of the video he threatens the life of a British hostage.
In the footage, Mr Sotloff reads out a text addressed to Mr Obama, saying: “You’ve spent billions of US taxpayers’ dollars and we have lost thousands of our troops in our previous fighting against the Islamic State, so where is the people’s interest in reigniting this war?”
Mr Sotloff, who had previously lived in Miami and worked for Time and Foreign Policy magazines, was last seen in Syria in August, 2013. He is thought to have been kidnapped near Aleppo, and to have been held in Raqqa. Friends said he had lived in Yemen for many years and spoke good Arabic.
The video, which is still to be fully authenticated, was reported initially by the SITE Intelligence Group, a US terrorism watchdog.
White House spokesman Josh Earnest last night said US officials were checking the reports.
The US has launched more than 120 air strikes in Iraq in the last month, in support of Kurdish forces attempting to curb the advance of IS militants and protect threatened minorities.
When he was first captured, Mr Sotloff’s family chose not to go public with details, on the advice of officials.
But his mother had pleaded for his release last week in a video directed at the IS group.
Addressing their leader Abu Bakr al-Baghdadi by name, Shirley Sotloff had said in a video that her son was “an innocent journalist” who should not pay for US government actions in the Middle East over which he has no control.
Last night, a family spokesman said Mr Sotloff’s family “knows of this horrific tragedy and is grieving privately”.
Unlike Mr Foley’s beheading, which was widely shared on Twitter accounts affiliated with the IS group, the video purporting to show Mr Sotloff’s killing was not immediately posted online, though several jihadi websites told users to expect it yesterday.
In Washington, a State Department spokeswoman said US intelligence analysis would “work as quickly as possible” to determine if the video of the beheading is authentic.
“If the video is genuine, we are sickened by this brutal act, taking the life of another innocent American citizen,” she said.
“Our hearts go out to the Sotloff family and we will provide more information as it becomes available.”
The spokeswoman said it was believed that “a few” Americans are thought to still be held by the IS but would not give any specifics.
Last night, Prime Minister David Cameron said the footage was an “absolutely disgusting, despicable act”. He added he will be making a statement on the video later but did not say when.
A Foreign and Commonwealth spokeswoman said later: “We are aware of a video which purports to be the murder of a US national and includes a threat to another hostage. We are urgently working to verify the authenticity of the video.”
The IS group, which has taken over a third of Syria and Iraq, has terrorised rivals and civilians alike with widely publicised brutality as it seeks to expand a proto-state it has carved out on both sides of the border