The report gives an insight into how Savile was able to gain a position of influence at the secure institution that included giving him keys to wards and allowing him to watch female patients undress to bathe.
"Savile could be charming and persuasive, at least to some, but at the same time he was grandiose, narcissistic, arrogant and lacking any empathy," it states. "He was also very manipulative, and many staff were convinced that he had close connections in high places and had the power to have them dismissed."
Una O'Brien, permanent secretary of the Department of Health, said in a statement that "inadequate processes" had allowed Savile to gain the position of authority at Broadmoor that aided his abusive behavior.
"While much has changed in the intervening years we will leave no stone unturned to make sure such appalling actions can never be repeated; our thoughts today are with the people who suffered and continue to suffer from these terrible crimes," she said.
The UK's NSPCC children's charity said more must be done to safeguard children and ensure that an apparent "culture of turning a blind eye" to abuse is not repeated.
"To hear that some hospital staff may have actively facilitated Savile's abuse of children is sickening and takes the scandal of his crimes to yet another abhorrent level," said Peter Watt, national services director for the charity.
"Savile escaped justice because people didn't want to hear or believe what children were saying. Ministers now need to be satisfied that this could never happen again and that children and vulnerable adults in hospitals or any government facility are safe today."
Savile died in October 2011 at age 84, soon after being treated in a hospital for pneumonia. His long history of abuse emerged only a year later, thanks to a TV documentary by UK broadcaster ITV.
The BBC, where he worked as a radio DJ and TV presenter, has set up a separate inquiry into abuses he carried out on BBC premises.