Jimmy Savile abused 60 people at Leeds General Infirmary, including at least 33 patients aged from five to 75, an independent investigation has found.
Savile also abused at least five individuals at high-security Broadmoor hospital, including two patients who were subjected to repeated assaults, a separate investigation discovered.
The chief executives of Leeds Teaching Hospitals NHS Trust and West London Mental Health NHS Trust, which covers Broadmoor, have apologised to victims.
In one of the most shocking disclosures, it was reported that Savile, who had publicly spoken of his fascination with the dead, had sexually abused bodies in the mortuary at Leeds, taking advantage of his role as a volunteer porter.
"The allegations about his behaviour in the mortuary are incredibly harrowing and disturbing," Sue Proctor, who led the investigation at Leeds, told reporters.
She said Savile, a one-time professional wrestler who became famous as a pioneering DJ in the 1960s, gave the account of his actions at the mortuary to a student nurse who worked at a different hospital.
"It was a quiet night and Savile was talking to this student nurse about what happened when it was quiet at Leeds general Infirmary and said that he went to the mortuary at night and played with the bodies, and committed sex acts on them," Ms Proctor said.
Savile's victims at Leeds General Infirmary (LGI) ranged from five years old to pensioners and included men, women, boys and girls.
Investigators at the hospital found that staff were told about some of the incidents but no allegations reached senior managers.
The inquiry into his activities at LGI after he started his association in 1960 included the testimonies of 60 people who gave accounts of their experiences with Savile to investigators - 33 of these were patients.
Three of these incidents were rapes, the investigators said.
The Leeds team said 19 of those who came forward were under 16 years old.
They said the majority of victims were teenagers but 19 victims were hospital staff - all women.
The inquiry panel said that he started working on the hospital radio service and he then became a regular visitor to the hospital, as a celebrity, a fundraiser and, from 1968, a volunteer porter.
It said Savile enjoyed unrestricted access to the hospital as he raised £3.5m through his charity activities. This gave him the opportunities he needed to indulge in abusive and inappropriate contact with patients and staff.
He had access to keys to various departments, had a series of offices in the hospital and even had access to the mortuary, the panel said.
The independent investigation interviewed more than 200 people and reviewed more than 1,300 documents covering the 50 years Savile was associated with LGI, which is now run by the Leeds Teaching Hospitals NHS Trust.
It found that the first case of abuse reported to the team happened in 1962 when Savile was 36. The most recent was in 2009 when he was 82.
The investigation panel found that incidents ranged from lewd remarks and inappropriate touching to sexual assault and rape.
Forty three of the encounters took place in public areas such as wards, corridors and offices.
The investigators found that nine victims told a member of staff about what happened either directly or through their parents at the time of the abuse. But they said none of these allegations were subsequently communicated to people in more senior positions.
Reporting their findings, the panel said: "It is clear from witness interviews that had senior managers at the hospital been made aware of Savile's abusive behaviour, they would have acted to stop it happening."
Chairwoman of the independent investigation Dr Sue Proctor said: "'Before saying anything about our findings, I want to commend the courage of those former patients, staff and visitors to Leeds General Infirmary who experienced abusive or inappropriate encounters with Savile.
"Because they came forward voluntarily and told us what happened to them, the NHS in Leeds and across the country now has an opportunity and an obligation to learn from their accounts and make sure that what happened in Leeds at the hands of Savile can never happen again.
"The NHS is in their debt and I am truly grateful to each of them."
Dr Proctor said: "For some, although the abuse took place decades ago, their experience endures as a painful and upsetting memory that still has an effect on them today."
Detectives have run an investigation into Savile in three strands - allegations involving Savile, those involving Savile and others, and those involving others.
A number of high-profile names have since been charged under the operation.
Further research by the NSPCC claimed at least 500 victims as young as two were abused by Savile.
The NSPCC report said the scale of Savile's offending inside Broadmoor was higher than previously thought, with Thames Valley Police having received 16 reports of abuse by him inside the special hospital.
It also describes how some awe-struck civil servants erroneously referred to the Top Of The Pops presenter as "doctor", unaware of the trauma he was inflicting on some youngsters behind hospital doors.
The figures show the most common age group for Savile's victims was 13 to 15.
In addition, fears that Savile abused children in more than 20 children's homes and schools across England are also being investigated.
Allegations dating back to the 1960s, 1970s and 1980s have been handed to the Department for Education following a review of documents by the Metropolitan Police.
UK Health Secretary Jeremy Hunt has apologised on behalf of the government and the NHS for letting down victims.