The apparent beheading was carried out by a man speaking with an English accent.
Foreign Secretary Philip Hammond today said the video appeared to be genuine, adding it was "an appalling example of the brutality of this organisation".
The militants threatened to kill another captive they also identified as an American journalist.
Separately, Mr Foley's family confirmed his death in a statement posted on a Facebook page that was created to rally support for his release, saying they "have never been prouder of him".
The statement attributed to the freelance journalist's mother Diane Foley said: "He gave his life trying to expose the world to the suffering of the Syrian people."
She implored the militants to spare the lives of other hostages: "Like Jim, they are innocents. They have no control over American government policy in Iraq, Syria or anywhere in the world."
The statement was posted on a Facebook page called "Find James Foley," which his family has used a number of times since his November 2012 disappearance.
Mr Foley, a 40-year-old journalist from Rochester, New Hampshire, went missing in northern Syria while freelancing for Agence France-Presse and the Boston-based media company GlobalPost.
The car he was riding in was stopped by four militants in a contested battle zone that both Sunni rebel fighters and government forces were trying to control. He had not been heard from since.
The video released on websites yesterday appears to show the increasing sophistication of the Islamic State group's media arm and begins with scenes of President Barack Obama explaining his decision to order airstrikes.
It then cuts to a bald man in an orange jumpsuit kneeling in the desert, next to a black-clad militant with a knife to his throat.
Mr Foley's name appears in both English and Arabic graphics on screen, and he is wearing a clip-on microphone as he begins his statement.
The scene is captured on at least two video cameras and has been edited in a professional style, and the sound quality is sharp.
At the end of the video, a militant shows a second man, who was identified as another American journalist, Steven Sotloff, and warns that he could be the next captive killed.
Mr Sotloff was kidnapped near the Syrian-Turkish border in August last year and freelanced for Time, the National Interest and MediaLine.
One US official said the video appeared to be authentic, and two other officials said the victim was Mr Foley.
One of the officials said Mr Obama was expected to make a statement about the killing on Wednesday.
The president was briefed about the video on Air Force One as he flew from Washington to resume his holiday on the island of Martha's Vineyard in Massachusetts. A White House statement said he would continue to receive regular updates.
The beheading marks the first time the Islamic State has killed an American citizen since the Syrian conflict broke out in March 2011, upping the stakes in an increasingly chaotic war.
If confirmed, the killing is likely to complicate US involvement in Iraq and the Obama administration's efforts to contain the group as it expands in both Iraq and Syria.
The group is the heir apparent of the militancy known as al Qaida in Iraq, which beheaded many of its victims, including American businessman Nicholas Berg in 2004.
The Islamic State militant group is so ruthless in its attacks against all people they consider heretics or infidels that it has been disowned by al Qaida's leaders.
In seeking to impose its harsh interpretation of Islamic law in the lands it is trying to control, the extremists have killed soldiers and civilians alike in horrifying executions - including mounting the decapitated heads of some of its victims on spikes.
Several senior US officials with direct knowledge of the situation said the Islamic State very recently threatened to kill Mr Foley to avenge the crushing airstrikes over the last two weeks against militants advancing on Mount Sinjar, the Mosul dam and the Kurdish capital of Irbil.
Both areas are in northern Iraq, which has become a key front for the Islamic State as its fighters travel to and from Syria.
Since August 8, the US military has struck more than 70 Islamic State targets - including security checkpoints, vehicles and weapons caches. It is not clear how many militants have been killed in the strikes, although it's likely that some were.
Officials from the State Department and Pentagon contacted social media sites to inform them of the video and ask them to remove it.
White House National Security Council spokeswoman Caitlin Hayden said the Obama administration asked the sites to "take appropriate action consistent with their stated usage policies".
In 2011, Mr Foley was among a small group of journalists held captive for six weeks by the government in Libya and was released after receiving a one-year suspended sentence on charges of illegally entering the country.
In a May 2011 interview about his experience, he recounted watching a fellow journalist being killed in a firefight and said he would regret that day for the rest of his life.
At the time, Mr Foley said he "would love to go back" to Libya to report on the conflict and spoke of his enduring commitment to the profession of journalism.
"Journalism is journalism," he said. "If I had a choice to do Nashua (New Hampshire) zoning meetings or give up journalism, I'll do it. I love writing and reporting."
The New York-based Committee to Protect Journalists estimates that about 20 journalists are missing in Syria.
GlobalPost chief executive and co-founder Philip Balboni asked "for your prayers for Jim and his family".
AFP chairman Emmanuel Hoog said the French news agency was "horrified" by the video and called Mr Foley "a brave, independent and impartial journalist".