Police had been hunting the 21-year-old since Saturday following the discovery of the bodies of his mother, stepfather and half-sister.
Detective Superintendent Chris Ward, of Thames Valley Police, said the force was now not looking for anyone else in connection with the victims’ murders.
The discovery of his body, about a mile from Oxford University, emerged after police released CCTV images showing his last known movements.
Captured at Oxford railway station, the footage showed him buying and bottle of water from a WH Smith store on the same day the bodies were discoverd.
Janet Jordon, 48, her six-year-old daughter Derrin and Philip Howard, 44, were found at their home in Didcot, Oxfordshire, at 8.20pm on Saturday. All three are believed to have been stabbed.
Detectives have confirmed that a knife, believed to be the murder weapon, has been recovered from the scene.
A major manhunt involving 120 officers was launched as officers combed the 70-acre Oxford University Parks and the surrounding area over the holiday weekend.
The public had been warned not to approach 6ft tall Allen, a former university groundsman, who had posted a series of photos of himself on social media sites holding knives.
Det Supt Ward said: “Members of the public reported finding the body of a man in a wooded area in Oxford, in Marston Road. This is an area that had not been previously searched by police as a result of this investigation.
“No formal identification has taken place but I am satisfied that this is the body of Jed Allen, who I had previously named as a suspect in this investigation. The members of all of the victims families have been informed, and they are being supported by specially trained officers.
“While the investigation into this matter will continue, I am not seeking anybody else in connection with the offence. I would like to offer my condolences to all of the families of the victims in this tragic case.”
The headteacher of Derrin’s school, All Saints Primary, earlier threw open the doors to welcome friends and well-wishers who wanted to pay tribute to the youngster. A community centre next to the school was opened to give local people a place to grieve together.
Headteacher John Myers said the reaction had been “devastation, shock, sadness”.
He added: “It’s just a combination of so many emotions, it’s such a terrible tragedy. Anybody’s life is precious and to lose parents and particularly a young girl in such a dreadful manner is truly awful.”
Mr Myers described Derrin as “beautiful, gentle, quiet, smiley, happy, precious, a lovely girl”.
The headteacher said there had been no indication of trouble in the family home, adding: “They were a perfectly normal, happy family.”