Jimmy Savile "would gratify himself sexually on BBC premises whenever the opportunity arose" and staff missed numerous opportunities to stop him, the long-awaited report into the scandal has found.
Dame Janet Smith's review found there was a culture of "reverence and fear" towards celebrities at the corporation and that "an atmosphere of fear still exists today in the BBC".
When a junior female employee at Television Centre complained to her supervisor that she had been sexually assaulted by Savile, she was told "keep your mouth shut, he is a VIP", the report found.
Dame Janet said girls who dared to complain about being sexually assaulted were regarded as "a nuisance" and their claims not properly dealt with.
BBC staff missed a string of opportunities dating back to the late 1960s to stop Savile, who died in October 2011 aged 84 never having been brought to justice for his crimes and is now believed to be one of Britain's most prolific sex offenders.
Dame Janet found that a number of BBC staff were aware of Savile's offending, but she cleared the broadcaster as a corporate body of knowing about it.
Her report states: "In summary, my conclusion is that certain junior and middle-ranking individuals were aware of Savile's inappropriate sexual conduct in connection with his work for the BBC.
"However, I have found no evidence that the BBC, as a corporate body, was aware of Savile's inappropriate sexual conduct in connection with his work for the BBC."
The report came as veteran DJ Tony Blackburn accused the BBC of making him a "scapegoat" after he was sacked on the eve of its publication.
Blackburn, 73, said "all relationships" he had with the BBC were "terminated with immediate effect" this week because his evidence to Dame Janet's review concerning an investigation in 1971 contradicted the BBC's own version of events.
He has pledged to take legal action against the corporation which he claims is making him a "scapegoat" for the "cover-up" of abuse.
Dame Janet's review looks at the culture and practices at the corporation during the years that Savile and fellow shamed broadcaster Stuart Hall, who has been in prison for sex attacks on under-age girls, worked there.
Savile raped and sexually assaulted 72 people, male and female, in connection with his work at the BBC dating back to 1959, while 21 people fell victim to Hall, 86, whose offending dates back to the 1960s, a report by Dame Linda Dobbs found.
Dame Janet said "Savile and Hall make very sorry reading for the BBC" and that the pair used their fame and charisma to prey on their mainly young victims.
Her report states: "Savile would gratify himself sexually on BBC premises whenever the opportunity arose and I heard of incidents which took place in virtually every one of the BBC premises at which he worked."
This included the BBC Theatre at Shepherd's Bush where Jim'll Fix It and Clunk Click were filmed, Television Centre where Top Of The Pops was filmed, and Broadcasting House.
Eight complaints about Savile's behaviour were made to BBC staff as early as the late 1960s, but each time they were brushed off or not escalated up the chain of command.
In late 1989 or early 1990 Savile stuck his hand up a female junior employee's skirt at Television Centre. The woman, referred to as C51, complained to her boss but was told "keep your mouth shut, he is a VIP".
More than a decade earlier, in November 1976, Savile was in front of the rolling cameras presenting Top Of The Pops when he put his hand under the bottom of a member of the audience next to him.
She leapt into the air and later complained to a BBC employee, but her accusation was shrugged off and she was told it was "just Jimmy Savile mucking about".
In the mid-1970s Ian Hampton, bass player with the pop group Sparks, also tried to raise the alarm. He had heard rumours that Savile had sex with under-age girls and spotted him leaving the Top Of The Pops studio with a young girl.
The guitarist alerted a BBC presenter, but was simply told not to be silly, while on another occasion he spoke to producer Robin Nash, but was told not to be ridiculous.
Dame Janet said there was a culture of not reporting complaints at the BBC from the 1970s right the way through to the 1990s, and a fear of saying anything that might "rock the boat".
She warned there was a particular fear of whistleblowing at the corporation and "I was told that an atmosphere of fear still exists today in the BBC".
She added: "As I have said, there was a culture of not complaining about anything. The culture of not complaining about a member of the Talent was even stronger.
"Members of the Talent, such as Savile, were to a real degree protected from complaint.
"The first reason for this is because of a deference or even adulation which was, and still can be, accorded to celebrity in our society. The second reason was because of the attitude within the BBC toward the Talent. The evidence I heard suggested that the Talent was treated with kid gloves and rarely challenged."
She added: "There was a feeling of reverence for them and a fear that, if a star were crossed, he or she might leave the BBC."
She criticised the hierarchy, rivalry and "macho culture" in parts of the BBC, and its complaints procedures.