The BBC has appointed former Appeal Court judge Dame Janet Smith and ex-Sky News boss Nick Pollard to lead two inquiries into Sir Jimmy Savile.
Police say Savile, who rose to fame in the 70s and 80s, may have sexually abused 60 people over a 40-year period.
Dame Janet will look into the culture and practices of the BBC during the years Jimmy Savile worked there.
Mr Pollard will examine Newsnight's shelving of an investigation into why police dropped a sexual abuse probe.
In a further move, the BBC is also to appoint an independent expert to look at sexual harassment claims and practices.
It comes after staff have come forward to make allegations about other inappropriate conduct to which they say they have been subjected over the years.
Police believe Savile, who died in October 2011 aged 84, may have sexually abused 60 people since 1959.
The BBC has been criticised for not calling Savile's behaviour into question and flagging up any abuse allegations during his long career at the corporation, during which he presented several television shows including Top of the Pops and Jim'll Fix It.
Dame Janet's inquiry will include evidence from people who have made allegations about being sexually abused by Savile on BBC premises or while on location for the corporation.
And it will hear from those who claim they raised concerns either formally or informally about his activities.
She will also look at "the extent to which BBC personnel were or ought to have been aware of unlawful and/or inappropriate conduct by Jimmy Savile on BBC premises or on location for the BBC".
The review will examine whether BBC culture enabled "the sexual abuse of children to continue unchecked". She will be assisted by an expert in child safeguards.
Dame Janet previously led the Shipman Inquiry, which examined the activities of GP Dr Harold Shipman who may have killed as many as 250 people.
The Pollard Review, which is being treated as a matter of urgency, will seek to establish whether there were any "failings" in the BBC's decision to drop the Newsnight investigation.
The programme had been looking into the CPS and Surrey Police's decision to drop an investigation of abuse claims against Savile.
It will also look at the BBC's handling of material which might have been of interest to the police. Mr Pollard will be given legal support independent of BBC management.
There has been speculation that it was dropped because the BBC was already planning to run more favourable programmes, claims which it has repeatedly denied.
BBC director general George Entwistle said last week he was launching the Newsnight inquiry to shake off the "clouds of suspicion".
In the review into sexual harassment, the independent expert - who has not been named - will help in "assessing claims of sexual harassment from the 1970s to the present day", with the aim of giving proper support to "anyone with a complaint".
The person appointed will work alongside the BBC's own human resources department to review sexual harassment policies and processes, and make any recommendations required.
Mr Entwistle said: "The allegations that have arisen in the last few weeks that date back decades have truly shocked me.
"I want to be absolutely sure that we have dealt with any cases from the past fairly and properly. If there are lessons we can learn then we must do so to ensure that the mistakes of the past should never be repeated."
Dame Fiona Reynolds, who chaired the BBC Executive Board which appointed the two inquiry heads, said: "These reviews will demonstrate the BBC's determination to open itself fully to scrutiny from independent experts, emphasising our belief that the basis of the public's trust is full openness and accountability."
Mr Entwistle did not take part in discussions around the decisions surrounding either the terms of reference for the reviews or the appointment of the two heads.
BBC Trust chairman Lord Patten has written to Mr Entwistle to confirm the acceptance of the details of the reviews.
He added: "The Trust take the allegations that have been made extremely seriously and wants you to make every effort to ensure that the inquiries have access to the resources they require to undertake their role comprehensively, as well as the full cooperation of BBC staff and executives."
Labour deputy leader Harriet Harman called for a single independent inquiry covering the BBC and other organisations Savile had contact with.
She said: "This is serious criminal sexual offending. We need to know why it went on so long and why was it not stopped.
"The idea we have got separate inquiries is a problem because we are looking at one man and how he manipulated the whole system.
"It is the government's responsibility to say 'this is very serious and it should be looked into independently'."
Meanwhile, a cafe at Stoke Mandeville Hospital in Aylesbury called Jimmy's in honour of Savile has been renamed Cafe@WRVS after the volunteering charity that runs it.
The cafe was opened by Savile in 2005.
At least one sexual assault by the entertainer is alleged to have occurred at the Buckinghamshire hospital.