The accusations include "sexual harassment, assault or inappropriate conduct" and involve both staff and contributors, according to the corporation. Some are so serious they have been reported to police.
The development will raise serious questions about the current culture within the BBC as well as its record during the 1970s and 1980s.
The admission came as BBC director-general George Entwistle faced a grilling from MPs amid allegations of a cover-up after bosses dropped a Newsnight investigation into Savile.
There was also further pressure on Newsnight editor Peter Rippon, who stepped aside earlier this week after the BBC said his explanation of why the investigation into Savile was dropped was "inaccurate or incomplete".
Last night it was reported an email existed from a Newsnight reporter in which Mr Rippon was accused of saying of the allegations "it was 40 years ago - the girls were not too young".
The deepening row followed a Panorama programme in which both the reporter and producer of the story criticised Mr Rippon's decision to axe the investigation.
Yesterday, MPs on the Culture, Media and Sport Committee urged Mr Entwistle to "get a grip" on his organisation.
He admitted there had been a culture at the BBC which "seemed to have allowed Jimmy Savile to do what he did". But he defended the organisation's handling of the scandal.
While the BBC had not done everything perfectly, Mr Entwistle said "we have done much of what we should have done and done it in the right order", since the scale of the crisis became clear.
However, he told MPs: "There's no question that what Jimmy Savile did and the way the BBC behaved – the culture and practices of the BBC seemed to allow Jimmy Savile to do what he did – will raise questions of trust for us and reputation for us. There's no question about that."
MPs expressed incredulity that Mr Entwistle did not inquire why Newsnight was investigating the Jim'll Fix It star.
The director-general said he did not "remember reflecting on it" and he wanted to be an impartial judge in any future disciplinary cases against BBC staff.
He also admitted it would take weeks before an inquiry into the Newsnight decision by Nick Pollard, former head of Sky News, would report its findings.
Members of the committee expressed serious concerns at the way the BBC has handled the scandal. Conservative MP Therese Coffey described as "chilling" an email sent by Mr Rippon last November that said "our sources so far are just the women" who had made the accusations.
Mr Entwistle said the choice of words was not "in the least defensible, of course".
However, he insisted he believed the culture at the broadcaster had changed since the 1970s and 1980s, although he added: "I'm not convinced it has changed as much as it should have."
Another member of the committee, Conservative MP Philip Davies, accused Mr Entwistle of a "determination not to show an undue interest" in the Newsnight story, despite planning a Christmas tribute to Savile.
He added: "It's not just a lack of curiosity – although it certainly is that – from somebody who has been a journalist, but given you are putting on these programmes, surely you must have wanted to ask whether or not you can stand something up on Newsnight, is it still appropriate for the BBC to be putting on tribute programmes to this person?"