He is Mohammed Emwazi, a Kuwaiti-born British man in his mid-20s from west London, who was previously known to British security services.
British police declined to comment, citing ongoing investigations.
Emwazi first appeared in a video last August, when he apparently killed the US journalist James Foley.
He was later thought to have been pictured in the videos of the beheadings of US journalist Steven Sotloff, British aid worker David Haines, British taxi driver Alan Henning, and American aid worker Abdul-Rahman Kassig, also known as Peter.
In each of the videos, the militant appeared dressed in a black robe with a black balaclava covering all but his eyes and top of his nose.
Speaking with a British accent, he taunted Western powers before holding his knife to the hostages' necks, appearing to start cutting before the film stopped. The victims' decapitated bodies were then shown.
Earlier this month, the militant featured in a video in which the Japanese journalist Kenji Goto appeared to be beheaded. Hostages released by IS said he was one of three British jihadists guarding Westerners abducted by the group in Syria. They were known collectively as "the Beatles".
Mohammed Emwazi timeline:
Source: Cage, London-based campaign group
'Jihadi John' movement mapped
Emwazi "claimed harassment"
In a news conference, Asim Qureshi, the research director of the London-based lobby group Cage, which had been in contact with Emwazi over a number of years, explained how he had been approached by the Washington Post for the story and detailed the difficulties Emwazi had had with security services in the UK and overseas.
Mr Qureshi said Emwazi, who is understood to be about 27, had been "extremely kind, gentle and soft-spoken, the most humble young person I knew".
He said he could "not be 100% certain" Jihadi John was Emwazi although there were "striking similarities".
Emwazi's difficulties began when he travelled to Tanzania in May 2009 following his graduation in computer programming at the University of Westminster, Mr Qureshi added.
He and two friends had planned to go on a safari but once they landed in Dar es Salaam they were detained by police and held overnight.
Emwazi then ended up flying to Amsterdam, in the Netherlands, where he claimed to be met by British intelligence agents from MI5 who accused him of trying to travel to Somalia, where the jihadist group al-Shabab operates. He denied the accusation and said the agents had tried to recruit him before allowing him to return to the UK.
Analysis: Frank Gardner, BBC News
US and British counter-terrorism officials discovered the identity of "Jihadi John" as far back as last September. The FBI, Britain's MI5 and other intelligence agencies used a combination of voice recognition software, interviews with former hostages and on-the-ground research in London to build up a profile of the man now revealed to be Mohammed Emwazi.
They have always declined to reveal the name for "operational reasons". Now that it's out in the public domain, it's emerged that Emwazi was well-known to MI5 and that it even tried to recruit him as an informer, years before he went off to Syria to eventually join Islamic State.
The practice by intelligence agencies of approaching jihadist sympathisers to work for them is likely to continue. It's believed both Britain and the US have informers inside the Islamic State "capital" of Raqqa. Yet this seems to have been little help in stopping the actions of Mohammed Emwazi, or bringing him to justice.
Profile: Mohammed Emwazi
Jihadist's 'typical trajectory'
Emwazi later moved to Kuwait, where he got a job at a computer company. But on a visit to London in 2010, he was detained by British counter-terrorism officials and prevented from flying back to Kuwait, his friends said.
"I had a job waiting for me and marriage to get started," Emwazi wrote in a June 2010 email to Cage.
"[But now] I feel like a prisoner, only not in a cage, in London," he added, "a person imprisoned and controlled by security service men, stopping me from living my new life in my birthplace and country, Kuwait."
Mr Qureshi said Emwazi had made persistent efforts to try to change his situation: "We had two-and-a-half years of communications talking about what he could do to alleviate his problems."
He said he did not know what had happened to Emwazi, adding: "When we treat people as if they are outsiders they will inevitably feel like outsiders - our entire national security strategy for the last 13 years has only increased alienation. A narrative of injustice has taken root."
Emwazi was believed to have travelled to Syria around 2013 and later joined IS, which has declared the creation of a "caliphate" in the large swathes of Syria and neighbouring Iraq it controls.
A spokeswoman for Prime Minister David Cameron would not confirm or deny the latest reports, adding that the police and security services were working hard to find those responsible for the murder of the British hostages.
The University of Westminster confirmed Emwazi had left six years ago, adding: "If these allegations are true, we are shocked and sickened."
The BBC's Rajini Vaidyanathan in Washington says the FBI went on record last September to confirm it knew who Jihadi John was. However, US officials said this month they would not name him as they believed this would be the best strategy for finding him and bringing him to justice.
A spokesman for the family of Steven Sotloff said: "We want to sit in a courtroom, watch him sentenced and see him sent to a super-max prison."
David Haines's sister, Bethany, welcomed the identification, but told ITV News: "I think all the families will feel closure and relief once there's a bullet between his eyes."
Jihadi John sightings
The masked Islamic State militant known as "Jihadi John", who has been pictured in the videos of the beheadings of Western hostages, has been named.