In May the 73-year-old pervert, who also worked at Hibernian FC, was jailed for six years and nine months after he admitted ten charges of indecent assault, one charge of lewd and libidinous behaviour and a breach of the peace.
McCafferty, from Northern Ireland, had preyed upon teenage boys between 1972 and 1996, and when sentenced was already serving a jail term for abusing a Belfast youth.
The series of offences in Scotland took place across the country in locations including hotel rooms, showers and buses.
Celtic has said it is conducting its own investigation into historic child sex abuse.
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This week’s payout to a former youth player, who cannot be named, comes after an action was raised in the Personal Injuries Court in Edinburgh.
The victim’s lawyer, abuse specialist Kim Leslie, claimed that until now Celtic had “denied responbility”, while the club has yet to issue a new comment on the case and its implicit admission of liability.
Ms Leslie said her client’s mental health had suffered as a result of McCafferty’s abuse against him in the 90’s.
She said: “For decades my client suffered as a result of McCafferty’s abuse, so above all else I’d like to pay tribute to him for the courage he has shown in stepping forward after coming to terms with what happened.
“I hope the successful end to this legal action brings closure to my client and also brings hope to those who considering a civil action of their own.”
McCafferty joined Falkirk in 2004 as a kit man before leaving the following year.
It is understood he had mostly basic administration as well as his kit duties at the club, and was based at the club’s base at Little Kerse.
At the time of his arrest in 2016 police had not received any complaints which coincided with his time at Falkirk FC.