The singer was arrested at his home in central London at 7.15am yesterday before being taken to a nearby police station.
Police have not yet revealed why the singer, whose real name is Paul Gadd, was arrested, saying only it is part of their Savile investigation.
The ageing rocker was spotted leaving Charing Cross police station shortly before 5pm yesterday.
A Scotland Yard spokesman said: "Officers working on Operation Yewtree have today arrested a man in his 60s in connection with the investigation. The man, from London, was arrested at approximately 7.15am on suspicion of sexual offences and has been taken into custody at a London police station.
"The individual falls under the strand of the investigation we have termed 'Savile and others'."
The spokesman added that Gadd had been released on bail to return in mid-December pending further inquiries.
Savile, who died last year at the age of 84, has been described as one of the most prolific sex offenders in recent UK history.
Scotland Yard detectives are dealing with 300 alleged victims and are following more than 400 lines of inquiry.
Gadd's arrest came as the chairman of the BBC Trust, Lord Patten, said he was dedicated to finding out the truth about the scandal that has engulfed the corporation, vowing there would be "no covering our backs".
He claimed the BBC's reputation was on the line and it had risked squandering the public's trust.
Speaking of Savile's apparent decades of criminality, he added: "Can it really be the case no-one knew what he was doing? Did some turn a blind eye to criminality? Did some prefer not to follow up their suspicions because of this criminal's popularity and place in the schedules? Were reports of criminality put aside or buried?
"Even those of us who were not there at the time are inheritors of the shame."
He also apologised "unreservedly" to the abused women who spoke to the BBC's Newsnight programme but did not have their stories told when the report was axed.
The BBC chairman said the two independent inquiries set up – one into the Newsnight report, the other into the BBC's culture and practices in the years Savile worked there – must get to the truth of what happened.
He said: "Now my immediate priority is to get to the bottom of the Savile scandal and to make any and every change necessary in the BBC to learn the lessons from our independent investigations."
Labour deputy leader Harriet Harman added there needed to be an over-arching independent inquiry into the Savile case.
She claimed the criminal justice system too often leads victims to believe they will not be believed if they come forward with allegations of sexual abuse, adding: "If there is an assumption you won't be believed then you are less likely to come and if you do come forward and then you meet that culture of dis-belief, then it is going to be swept under the carpet."
However, Justice Secretary Chris Grayling said he was not convinced by the case for an immediate judge-led inquiry of the kind she proposed.
He said: "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."
There were also claims yesterday that former BBC director general Mark Thompson's office was twice alerted about the Savile abuse claims, despite his insistence he had no personal knowledge of the allegations.
Reports suggested his aides were told of the claims of abuse on BBC premises in May and September but his spokesman denied the claims were ever passed on to Mr Thompson.
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