Dozens of women have come forward to say that Savile, who died in October 2011 aged 84, sexually assaulted them when they were as young as 13. London's Metropolitan Police, which is leading a national investigation, says it has identified 40 potential victims.
The publicly funded national broadcaster is facing questions about its failure to stop Savile's predatory behavior, which was an open secret in showbiz circles during his heyday several decades ago.
BBC Director-General George Entwistle announced late Friday that the broadcaster would hold an inquiry into the "culture and practices of the BBC during the years Jimmy Savile worked here."
"It will examine whether that culture and those practices allowed him or others to carry out the sexual abuse of children," said Entwistle, promising a "forensic but also soul-searching examination."
Some assaults are alleged to have taken place on BBC premises, others at hospitals and schools Savile visited as part of his charity fundraising.
Entwistle said he offered a "profound and heartfelt apology on behalf of the BBC to every victim."
"As the director-general of the BBC I have made clear my revulsion at the thought that these criminal assaults were carried out by someone employed by the BBC and that some may have happened on BBC premises as well as, we now discover, in hospitals and other institutions across the U.K.," he told reporters.
Entwistle -- who has been in his job for less than a month -- said the BBC would also investigate why a report on Savile by its "Newsnight" program was dropped at the last minute in December for what the broadcaster called "editorial reasons."
The allegations against Savile were eventually aired in a documentary broadcast earlier this month on the rival ITV channel.
The British government said it would hold its own investigation into how Savile was appointed to lead a taskforce overseeing management restructuring at Broadmoor psychiatric hospital in the 1980s. Former patients at the hospital have claimed Savile abused them.
"In hindsight he should very obviously not have been appointed," the Department of Health said in a statement.
Savile, known for his platinum hair, garish tracksuits, chunky gold jewelry and ever-present cigars, was a fixture on British TV between the 1960s and the 1990s as host of music show "Top of the Pops" and children's program "Jim'll Fix It."
He was knighted by both Queen Elizabeth II and the Vatican for his charity work, but his reputation has been in free-fall since the abuse allegations were made public. Last week his family removed the headstone from his grave in Scarborough, northeastern England, and destroyed it, "out of respect for public opinion."
The granite tombstone bore the words "It was good while it lasted."