The cigar-smoking TV celebrity, known for his lurid tracksuits and gold jewellery, abused the child during a visit to the hospital in the 1970s.
Savile, who was knighted in 1990, is also thought to have sent his bodyguard to a student nurse’s room at midnight, telling her: “Jimmy is ready for you now.”
Now, Humberside Police and Humber NHS Foundation Trust are passing their conclusions to Operation Yewtree, the Metropolitan Police’s investigation uncovering abuse on an “unprecedented scale”.
A trust spokesman said: “The conclusion by Humberside Police and the author is that the event involving the patient took place.
“The author has further concluded that the event involving the former student nurse is likely to have taken place.
“The trust would like to express its deep sorrow and sympathy to all victims.”
Savile is thought to abused 450 victims at hospitals, the BBC and groups all over the UK, using his charity work and celebrity status to cloak his depravity.
After receiving a letter from the Department of Health in February 2014, the NHS trust launched an investigation with the police’s Protecting Vulnerable Persons Unit into Savile’s behaviour at the legacy hospital, which closed in 1997.
As well as caring for patients with mental illnesses, De La Pole also had an orthopaedic ward.
The patient told investigators he had taken a bath and had returned to the patients’ lounge, where Savile was standing with a nurse. The boy returned to the bathroom upstairs after he was asked to clean the bath and was followed by Savile.
The report stated: “Savile started to talk to him, saying something like he was a good kid.”
Savile pushed the boy against a sink and subjected him to a serious sexual assault while the boy heard “what he assumed to be Savile’s jewellery rattling.”
A woman who was a student nurse contacted the trust after allegations against the former presenter of Jim’ll Fix It started coming to light after his death in 2011.
She was a student nurse when Savile visited Baynard House at De La Pole Hospital, Willerby, to present a minibus in the 1970s and the celebrity stayed the night in the student accommodation block.
The trust report said: “At around midnight, Savile’s bodyguard knocked on her door and told her, ‘Jimmy is ready for you now.’ She told him to go away.
“She said nothing happened for it to be reported to the police as far as she is concerned and that it was treated as a joke at the time.
“She nevertheless felt, in view of the publicity having emerged in 2012 and 2013, she should make someone aware of it.”
Humberside Police say there is “not sufficient evidence” to carry out further investigations to see if anyone else was targeted by Savile.
The trust spokesman said: “This will be assessed on a case-by-case basis should the trust receive any future disclosures.”
Scale of abuse ‘unprecedented’
Savile is thought to have targeted hundreds of people, ranging from young girls and boys to adults while mixing in royal circles and revelling in his public image.
Operation Yewtree was launched by the Met in October 2012 and described the abuse as being “on an unprecedented scale”, with the number of potential victims “staggering”.
During his lifetime, two police investigations had looked into reports about Savile, the earliest known being in 1958, but he was never charged.
A report into sexual abuse at the BBC, prompted by the Savile scandal, is expected to be published next week.