He was found dead in his cell at Durham’s Frankland Prison in October having been disembowelled.
He will be sentenced on July 12.
Nathan Mann, 23, is also charged with Harrison’s murder, but he did not appear before the court.
After his murder, Harrison’s family released a statement saying: “Although we never condoned his past actions, he was serving his time and was by all accounts a model, trusted prisoner who did not deserve to die in this horrific way.”
The unsuspecting youngster had accompanied him back to his flat where he said he was going to get money for cigarettes and drink.
But once he had lured her inside he ordered the terrified girl to strip and raped her twice. She managed to escape when another man arrived and was found naked in the street with her clothes in her arms.
The pervert was jailed indeterminately at Carlisle Crown Court as it was the third time he had been involved in sex attacks on young girls.
At the age of 13, Harrison got a formal police warning for indecently assaulting a seven-year-old in an incident which would now be classed as rape. And two years later he was in court for threatening to rape a 15-year-old girl whose breasts he grabbed during a lesson.
In the 13-year-old schoolgirl rape case, Prosecutor Rob Dudley said Harrison had sexual activity with another underage teenager just a few days before the attack.
Judge Peter Hughes, QC, said Harrison had to be locked up for public protection because he posed a substantial risk to young girls.