Police have recorded hundreds of allegations of sexual abuse by Savile, who presented the first Top of the Pops in 1964 and returned several times to front the show, including for its last episode.
Digital channel BBC Four has been showing complete archive episodes of Top of the Pops since last April, starting with an episode from April 1976.
A BBC spokesperson confirmed to the Daily Mail: "We will no longer show Jimmy Savile presenting Top of the Pops.
"We will assess carefully the editorial justification for any other Savile appearances. This decision was taken after allegations first came to light from the ITV documentary."
Savile groped a 19-year-old audience member on air during the November 25, 1976 edition of the music show.
"The worst thing was that he was so casual when he did it," said Sylvia Edwards. "He was committing a sexual assault live on the BBC and no-one gave a damn."
Plans for the 2012 seasonal Top of the Pops special will still go ahead, with an insider adding to the Daily Mail: "It's very unfortunate, but it would be disappointing if the disgusting behaviour of one man impacted on the reputation of a legendary show like TOTP."