Scarborough Borough Council said work to dismantle the memorial headstone, which bears Savile's image and lists his accomplishments, was carried out shortly after midnight.
Savile's family said they made the decision to ensure the "dignity and sanctity" of Woodlands Cemetery in Scarborough.
The triple headstone was removed from the cemetery overnight to avoid a "circus" and will now be destroyed, funeral director Robert Morphet said.
Morphet said Savile's family had made the decision because of "the impact the stone remaining there could have on the dignity and sanctity of the cemetery".
Initially the stone was due to be removed this morning.
Morphet, who organised Savile's funeral and oversaw the dismantling of the headstone last year, said: "We felt the most dignified way to do it would be discreetly, quietly and while it was dark."
The headstone, which was inscribed with the epitaph "It Was Good While It Lasted" and verses composed by a family friend, will now be destroyed, the BBC reported.
Savile had a long association with Scarborough and was buried there after his death, aged 84, in October 2011.
The grave would remain unmarked for the moment, he said.
On Tuesday, the Metropolitan Police said it was pursuing 120 separate lines of inquiry after recording eight allegations against the Leeds-born entertainer, including two accusations of rape.
Scotland Yard said there could be as many as 30 victims over 40 years. It said Savile had a "predilection for teenage girls" and the pattern of offending behaviour was on "a national scale".
The investigation follows claims made about the BBC broadcaster in an ITV documentary last week.
BBC Director General George Entwistle has promised a "comprehensive examination" of the allegations concerning Savile's time at the corporation.
The removal of the headstone comes days after a footpath sign in Scarborough commemorating Savile was taken down by the borough council.
A plaque outside his flat in Scarborough was also removed last week after the words "rapist" and "paedophile" were written on it.
British Prime Minister David Cameron has already urged the BBC and the police to investigate fully claims of sexual abuse against Savile.
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