The 64-year-old radio and TV star was quizzed by police linked to Operation Yewtree - the specialist unit probing claims against Jimmy Savile.
Gambaccini was arrested by officers at his penthouse apart-ment on London's South Bank early on Tuesday morning.
A 74-year-old was also arrested at a separate south London address.
The men - the 15th and 16th arrests as part of Yewtree - have been bailed until January pending further inquiries.
A Metropolitan Police spokesman said: "On Tuesday, October 29 a 64-year-old man was arrested.
"The man was arrested at an address in south London on suspicion of sexual offences and taken into police custody."
Detectives have run Yewtree in three strands - allegations involving Savile, those involving Savile and others, and those involving others.
The claims against both men arrested on Tuesday are being dealt with under the "others'' strand so are not related to Savile.
Gambaccini, who has dual UK and US nationality, presents America's Greatest Hits on Saturday nights on BBC Radio 2.
The BBC News website confirmed his arrest on suspicion of historic sexual offences.
The Metropolitan Police refused to confirm his identity.