The video, titled "A Message To America," was posted on social media websites. It was not immediately possible to verify its authenticity.
Foley, who has reported in the Middle East for five years, was kidnapped on Nov. 22, 2012, by unidentified gunmen. Steven Sotloff, who appeared at the end of the video, went missing in northern Syria while he was reporting in July 2013.
A Twitter account set up by Foley's family to help find him said early on Wednesday: "We know that many of you are looking for confirmation or answers. Please be patient until we all have more information, and keep the Foleys in your thoughts and prayers."
The White House said that U.S. intelligence agents were working to verify the authenticity of the video.
Islamic State, an al-Qaeda offshoot, had not previously executed American citizens publicly. The Sunni militant group has declared a caliphate in parts of Iraq and Syria in areas it controls.
The video, which was posted after the United States resumed air strikes in Iraq for the first time since the end of the U.S. occupation in 2011, opened with a clip of U.S. President Barack Obama saying he had authorised strikes in Iraq.
"Obama authorises military operations against the Islamic State effectively placing America upon a slippery slope towards a new war front against Muslims," words appear in English and Arabic on the screen.
It showed black and white aerial footage of air strikes with text saying "American aggression against the Islamic State"
A person identified as James Foley and wearing an orange outfit is seen kneeling in the desert as a man in black dress with a black mask stands beside him, holding a knife.
"I call on my friends family and loved ones to rise up against my real killers, the U.S. government, for what will happen to me is only a result of their complacency and criminality," the kneeling man says.
The man in the mask speaks in a British accent and says: "This is James Wright Foley, an American citizen, of your country. As a government, you have been at the forefront of the aggression towards the Islamic State."
"Today your military air force is attacking us daily in Iraq. Your strikes have caused casualties amongst Muslims. You are no longer fighting an insurgency. We are an Islamic army, and a state that has been accepted by a large number of Muslims worldwide."
Following his statement he beheads the kneeling man.
At the end of the video, words on the side of the screen say "Steven Joel Sotloff" as another prisoner in an orange jumpsuit is shown on screen.
"The life of this American citizen, Obama, depends on your next decision," the masked man says.
Foley, a freelance reporter, had been covering Syria's civil war for GlobalPost. In 2011, he was held for 45 days by forces loyal to former Libyan leader Muammar Gaddafi.
Sotloff is also a freelancer journalist with published stories in Time Magazine and Foreign Policy. He has worked in Syria, Libya and Yemen.
Islamic State has executed hundreds of people in Syria and Iraq during its advance. Its members follow a hard line interpretation of Sunni Islam but target all those who oppose it, including Sunni Muslims.
The Syrian Observatory for Human Rights, a monitoring group, said Islamic State militants had executed 700 members of a Sunni tribe in eastern Syria in two weeks, the majority of them civilians.
White House spokeswoman Caitlin Hayden said: "We have seen a video that purports to be the murder of U.S. citizen James Foley by ISIL. The intelligence community is working as quickly as possible to determine its authenticity.
"If genuine, we are appalled by the brutal murder of an innocent American journalist, and we express our deepest condolences to his family and friends."
Islamic State also released another video on Tuesday that gave the strongest indication yet it might attempt to strike American targets.
The video with the theme "breaking of the American cross" boasts Islamic State will emerge victorious over "crusader" America.
It follows a video posted on Monday, warning of attacks on American targets if Washington struck against its fighters in Iraq and Syria.
The latest footage spoke of a holy war between Islamic State and the United States, which occupied Iraq for nearly a decade and faced stiff resistance from al-Qaeda.
Unlike al-Qaeda, Islamic State has so far focused on territorial gains designed to eventually establish a full-blown Islamic empire.
Islamic State's sweep through northern Iraq, bringing it close to Baghdad and in control of the second city, Mosul, drew U.S. air strikes on the country for the first time since the end of the American occupation in 2011.
U.S. air strikes have helped Kurdish peshmerga fighters who held parts of the north regain some territory captured by the Sunni militants.