The report said Savile abused his victims at 14 medical sites including the Leeds hospital and the Wheatfields hospice in the Headingley district, which is run by the Sue Ryder charity.
Savile is said to have assaulted a victim at the hospice in 1977.
A total of 450 people have come forward alleging sexual abuse against Savile since October, and within the recorded crimes, there are 34 rapes and 126 indecent acts, the police and NSPCC report said.
Of his victims, 73% were children, with the total victim age range between eight and 47 years old at the time of the offences.
The police report found that the earliest reported offence committed by Savile was in Manchester in 1955, and the final reported allegation was in 2009.
The offences cover the period when Savile worked at the BBC between 1965 and 2006 and include allegations linked to the final recording of Top of the Pops.
They also involve the period when he worked at Leeds General Infirmary between 1965 and 1995.
Abuse at Stoke Mandeville Hospital took place between 1965 and 1988, while at Duncroft School, a children’s home, the allegations cover a period between 1970 and 1978.
The peak was between 1966 and 1976, when he was aged between 40 and 50.
Helen Ankrett, palliative care services manager at Sue Ryder’s Wheatfields Hospice, said: “Jimmy Saville was well known locally for his fundraising efforts for local charitable causes and as such I’m aware that in the first few years of Wheatfields Hospice’s opening, he organised a few fundraising events in aid of the hospice.
“We’re appalled and dismayed to hear that an alleged incident took place on the premises of the hospice in 1977. Our thoughts are with the individual involved and their family at this difficult time, and we will of course fully support the police in their investigation.”
Leeds Teaching Hospitals said it would look into any complaints made to police about incidents at Leeds General Infirmary and St James’s University Hospital, where Savile worked as a volunteer and fundraiser.
It said it would also investigate information given directly to the Trust about this “extremely distressing subject”.
A spokesman for the Leeds Teaching Hospitals NHS Trust said: “In early December, the Trust published the terms of reference for its internal investigation into matters relating to Jimmy Savile’s long-standing involvement with the Leeds Teaching Hospitals as a volunteer and fundraiser.
“This will be a thorough and detailed piece of work and will be carried out in conjunction with parallel investigations by the Department of Health and other NHS trusts. Work is now under way and we expect our report will be ready towards the end of this year.
“As part of this work our panel will look at approaches from people who have contacted the Trust directly to share information on this extremely distressing subject.
“The panel will also examine in detail any information the police pass to us about incidents reported to them at Leeds General Infirmary and St James’s University Hospital.”
Savile’s main home was a luxury flat overlooking Roundhay Park in Leeds.
The police and NSPCC report said Savile’s offending presents “a potential watershed”.
It concluded that Savile was an “opportunistic individual who used his celebrity status as a powerful tool to coerce and control” his victims.
The report said it would be “naive” to view the case as the isolated behaviour of a “rogue celebrity” - but the “context of the 1960s and 1970s” need to be recognised.
“It was an age of different social attitudes and the workings of the criminal justice system at the time would have reflected this,” it said.
But the report stopped short of apportioning blame to other institutions and agencies that may have “missed past opportunities” to stop Savile.