It is understood to be the first BBC settlement to be made public following the Savile scandal.
The victim, now 54, was a desperately unhappy child living in a care home when he wrote to Savile telling the DJ of the difficulties of growing up in the Northern Ireland Troubles.
In a heartfelt letter, he also confided to the then BBC star that he had been the victim of sexual abuse in the home and longed to meet Abba or Boney M on the hit show.
Savile responded by sending money to pay for the boy to travel to the studio but then handed him over to an accomplice who repeatedly molested him.
The man, who we are calling Robert, has already given evidence to the Dame Janet Smith inquiry into Savile’s abuse at the BBC.
The corporation initially denied responsibility, saying that because he was not abused by Savile he was not eligible for compensation.
However it has now accepted that there was a potential for a finding of negligence and made the £15,000 settlement.
The BBC would not reveal whether any other payments had been made to other individuals, although a scheme has been set up to compensate victims.