It is also a year to the day since Savile died, aged 84, at his home in Leeds.
Scotland Yard detectives are currently dealing with about 300 alleged victims and are following more than 400 lines of inquiry as part of their Operation Yewtree investigation into “Savile and others”.
Dame Janet, who was appointed to the appeal court in 2002, led the inquiry into the activities of serial killer GP Dr Harold Shipman, which reported in 2005.
She will be examining allegations from people who claim they were sexually abused by Jimmy Savile on BBC premises, or while working on location for the corporation, and will gather evidence from those who claim they raised concerns about his activities.
The chairman of the BBC Trust, Lord Patten, said he was committed to finding out the truth about the scandal that has engulfed the corporation, vowing there would be “no covering our backs”.
He also apologised “unreservedly” to abused women who spoke to a BBC’s Newsnight investigation into the abuse which was axed last year.
A separate inquiry into possible BBC management failures over the canning of the Newsnight programme has already began under former head of Sky News Nick Pollard.
Labour deputy leader Harriet Harman on Sunday called for an over-arching independent inquiry into the Jimmy Savile case.
But Justice Secretary Chris Grayling said he was not he was not in favour of an immediate judge-led investigation: “There is always a danger if you set up a very substantial inquiry process of that kind that it takes much longer to get to the truth.”
Gary Glitter, whose real name is Paul Gadd, has been bailed to reappear at a police station in mid-December this year, pending further inquiries.