Most of the alleged offenses were committed around the city of Leeds, where Savile lived, and in London, where he worked.
The peak of offending reported to police was between 1966 and 1976, when Savile was between 40 and 50 years old.
Separately, a review by the Crown Prosecution Service was critical of the decision by two police forces not to file charges against Savile after investigating four separate allegations of sexual abuse.
In 2007 and 2008 Surrey Police investigated three complaints that he had engaged in sexual behavior with young girls. During the same period, Sussex Police investigated a complaint by a young woman.
Alison Levitt, chief legal adviser to the Director of Public Prosecutions, said police were too cautious in their approach and should have asked more questions to push inquiries forward.
The alleged victims and their accounts were treated "with a degree of caution which was neither justified nor required," she said.
"Having spoken to the victims I have been driven to conclude that had the police and prosecutors taken a different approach a prosecution might have been possible."
Peter Watt, director of child protection advice for the NSPCC, said the scale of Savile's abuse "simply beggared belief."
But, he added, one positive is that nearly 800 additional children have been protected from abuse because the publicity around the Savile case has encouraged people to call the charity's helpline.
For many, it's the first time they've spoken out about abuse, he said.
"We are optimistic that this signals a watershed moment for child protection in this country. We must seize the opportunity if we are to make a lasting change," he said.
The report's authors acknowledge that it is too late to act on the claims against Savile, but they say the investigation met "the need for hundreds of victims to have official recognition of the serious crimes they have suffered and to know they have been taken seriously."
Millions of Britons who grew up watching Savile on TV's "Top of the Pops" and "Jim'll Fix It" were shocked by the fall from grace of an entertainer who'd been awarded knighthoods by Queen Elizabeth II and the late Pope John Paul II for his charitable work.
Savile died in October 2011 at age 84, soon after being treated in a hospital for pneumonia. His death was followed by a series of glowing tributes, including BBC specials.