The broadcaster is alleged to have sexually abused 60 people from as far back as 1959.
Former High Court judge Dame Janet Smith will focus on the culture and practices of the BBC while Savile worked at the corporation.
Nick Pollard - former Head of Sky News - will lead the inquiry over a cancelled investigation into Savile by Newsnight.
Smith's investigation will also look into the BBC's current child protection and whistleblowing procedures.
The Pollard Review will be treated as an urgent inquiry, and will "seek to establish whether there were any failings in the BBC's management of the Newsnight investigation relating to allegations of sexual abuse of children by Jimmy Savile, including the broadcast of tribute programmes on the BBC".
The inquiry will also focus on how the BBC handled any files that may have been of police interest.
The pair were appointed by the BBC Executive Board, with chair Dame Fiona Reynolds saying: "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."
Culture Secretary Maria Miller has said that Newsnight "inappropriately" axed an investigation into child abuse allegations against Sir Jimmy Savile.
In pictures - Jimmy Savile's life and career:
Copyright: flickr/BBC Pictures