He was held at his home in central London yesterday and taken to a police station.
A Scotland Yard spokesman said: "Officers from Operation Yewtree have arrested a man in his 60s in connection with the investigation.
"The man, from London, was arrested at 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'."
Glitter, whose real name is Paul Gadd, was photographed leaving Charing Cross police station shortly before 5pm yesterday. Scotland Yard was not available for comment on his release, and police did not say what led to his arrest.
The late TV presenter 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 about 300 alleged victims and are following more than 400 lines of inquiry.
It emerged yesterday that Savile's cottage in Allt na Reigh, Glencoe, Scotland, was vandalised overnight.
A spokesman for the Northern Constabulary said "abusive slogans" were painted on the walls of the property.
Last week police searched the cottage to look for "any evidence of any others being involved in any offending".
Glitter'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 said the BBC's reputation was on the line, and that it has risked squandering the public's trust.
Speaking of Savile's apparent decades of criminality, he wrote: "Can it really be the case that 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? 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 – 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.