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.
It is understood the payments will be made following Dame Janet’s inquiry.
Robert told how he wrote to the DJ in 1977 saying he wanted to meet the bands.
He said: “When I arrived I was shown to his room at Television Centre and met him and there were other small children present.”
Robert added that Savile had a young girl of about eight on his knee and looked aroused.
“I ran out and tried to get help and asked the security men at reception to help but an assistant of Savile’s turned up and took me back to his room with security. I had been so used to being sexually abused I knew what was to come. A man in his 40s or early 50s joined us, sat behind me and said he would be taking care of me.”
Almost immediately the man, called Brian, began sexually abusing him and later took him outside to a waiting car where he was taken to an exclusive club in central London.
“At this house (the club) Brian abused me and a much smaller boy aged between seven and nine who looked very poorly and thin and was also being abused by a very obese man.”
He believes that he was drugged and has no recollection of being abused by Savile but woke up the next morning facing the smaller child.
“Savile came in, and took the other boy away and said I should hurry up to have breakfast. I had breakfast and Savile made me a lunch box.”
He was then taken to Victoria Station and given £5.
He later returned to the children’s home in Northern Ireland, which has itself been the subject of a public inquiry into abuse.