The hour-long documentary lifts the lid on the extent to which the higher echelons of the corporation were aware of the claims against the late DJ.
BBC foreign editor John Simpson describes the scandal as "the worst crisis that I can remember in my nearly 50 years at the BBC".
Newsnight editor Peter Rippon maintains the piece - which was due to run last December - was pulled for editorial reasons, and not because the potentially damaging revelations coincided with a planned tribute to the star.
But tonight, the hour-long documentary will hear from Newsnight producer Meirion Jones and reporter Liz MacKean, who both claim they had interviewed at least four alleged victims of Savile - and confirmed with Surrey Police that they had investigated sex abuse complaints against the Jim'll Fix It star in 2007.
They say that when they told bosses the Crown Prosecution Service did not charge Savile because of insufficient evidence, they were told to end the investigation - and the show was withdrawn.
The horror stories about Savile only fully emerged after ITV broadcast a documentary at the start of this month - sparking mayhem at the BBC over losing its scoop and leading to the allegations of a cover-up.
A Panorama statement said: "Peter Rippon has always maintained the story was pulled for 'editorial reasons' and not because of a potentially embarrassing clash with planned BBC tributes to Savile over Christmas.
"Panorama has found no evidence to contradict that view."
Simpson said of the fallout: "This is the worst crisis that I can remember in my nearly 50 years at the BBC. I don't think the BBC has handled it terribly well.
"I mean I think it's better to just come out right at the start and say we're going to open everything up and then we're going to show everybody everything.
"All we have as an organisation is the trust of the people the people that watch us and listen to us and if we don't have that, if we start to lose that, that's very dangerous I think for the BBC."
Panorama, which airs at 10.35pm on BBC1, also probes why BBC chiefs gave different explanations over the nature of the documentary and why it was dropped.
In the aftermath, Director General George Entwistle wrote to all staff saying the Newsnight investigation was into "Surrey Police's enquiry into Jimmy Savile towards the end of 2011".
Mr Jones immediately emailed Mr Entwistle countering that, writing: "George - one note - the investigation was into whether Jimmy Savile was a paedophile - I know because it was my investigation.
"We didn't know that Surrey police had investigated Jimmy Savile - no-one did - that was what we found when we investigated and interviewed his victims."
Then in an interview David Jordan, the BBC's Head of Editorial Policy, said: "They (Newsnight) were investigating the Surrey Police investigation into Jimmy Savile and they discovered that Surrey Police had done a perfectly decent investigation into Jimmy Savile, had made recommendations to the CPS and then subsequently it had been dropped because of lack of evidence."
Mr Jones and Ms MacKean tell the programme makers their bosses wanted them to stand up a suggestion that Savile was not prosecuted because the Crown Prosecution Service thought he was too old and frail.
When it emerged that was not true and he was not prosecuted because of insufficient evidence the pair were told to abandon the investigation rather than get more proof, Panorama reports.
Ms MacKean said: "Ever since the decision was taken to shelve our story I've not been happy with public statements made by the BBC.
"I think they're very misleading about the nature of the investigation we were doing."
The Newsnight journalists had filmed Karin Ward, a key witness, in mid-November saying Savile abused her during her time at Duncroft approved school.
She claims she saw Gary Glitter having sex with another under-age girl from Duncroft on BBC premises.
Ms Ward has agreed that Panorama can broadcast clips from the interview for the first time in the programme Jimmy Savile: What the BBC Knew.
Newsnight quoted three other unnamed former Duncroft pupils who said they were also sexually abused by Savile. The script also included a report of sexual abuse of a teenager at Stoke Mandeville hospital.
Ms MacKean said Mr Rippon suddenly went cold on the story: "All I can say is that it was an abrupt change in tone from, you know, one day 'excellent, let's prepare to get this thing on air' to 'hold on'."
Ms MacKean says she was left with the clear impression her editor was feeling under pressure, writing to a friend: "PR (Peter Rippon) says if the bosses aren't happy... (he) can't go to the wall on this one."
Ms MacKean told Panorama: "I was very unhappy the story didn't run because I felt we'd spoken to people who collectively deserved to be heard and they weren't heard and I thought that was a failing...I felt very much that I'd let them down."
The programme also reveals that BBC Director of News Helen Boaden told Mr Entwistle - at that time Director of Vision - during an awards lunch on December 2 about the Newsnight investigation and its possible impact on planned tributes to Savile.
She told him that, if the Newsnight investigation went ahead, he might have to change the Christmas schedules.
Mr Jones e-mailed Mr Rippon five days later to warn him about what would happen if the investigation was dropped.
"I was sure the story would come out one way or another and that, if it did, the BBC would be accused of a cover-up," Mr Jones tells Panorama.
"In fact I wrote an email to Peter saying 'the story is strong enough' and the danger of not running it is 'substantial damage to BBC reputation'."
Two days later Mr Rippon decided to kill the investigation, Panorama reports.
The Panorama investigation also hears new evidence of suspicions within the BBC about Savile's activities as far back as the early 1970s.
Former Nationwide reporter, Bob Langley, was sent to cover one of Savile's many charity runs for the programme. On two occasions he spotted young girls coming out of Savile's caravan.
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