The findings, compiled by the Metropolitan Police and NSPCC under Operation Yewtree, concluded that 214 crimes have been recorded across 28 force areas - a scale of crime "unprecedented" in this country.
It also revealed that one offence was committed at Broadmoor Hospital, in Crowthorne, where Savile held a position on the hospital board and had an office and flat inside the main part of the high-security facility.
Savile's six decade-long reign of terror lasted from 1955 to 2009, when he was 82 years old.
Detective Superintendent David Gray of the Metropolitan Police's paedophile unit, who is leading the investigation, said: "Perhaps the most important learning from this appalling case is in relation to the children and adults who spoke out about Jimmy Savile at the time. Too often they were not taken seriously.
"We must not allow this to happen again - those who come forward must be given a voice and swift action taken to verify accounts of abuse."
Savile's youngest victim was eight years old at the time of abuse and the oldest 47. Of those, 82% are female and the majority were aged 13-16.
Det Supt Gray added: "The details provided by the victims of his abuse paint the picture of a mainly opportunistic individual who used his celebrity status as a powerful tool to coerce or control them, preying on the vulnerable or star-struck for his sexual gratification."