ReutersLawyers say more than 20 legal claims of historical abuse at Celtic Boys Club have been settled for a seven-figure sum.
About 30 former players had launched a class action against Celtic Plc for damages.
Thompsons Solicitors said that 70% of those cases had now been settled and that further settlements are expected in the coming weeks.
Celtic had indicated last year that it was seeking to settle the cases.
Several former coaches and officials at the boys club have been convicted in recent years of sexual offences against teenage players spanning decades.
In 2023, a judge gave the go-ahead for a US style "class action" group litigation to proceed against Celtic for alleged abuses at Celtic Boys Club.
The boys club was established as a feeder team to the senior Celtic side in 1966 and the two clubs had close ties, sharing players, officials and premises.
Celtic had always insisted that it was not responsible because the boys club was an "entirely different organisation".
But lawyers acting for the former players argued that the boys club and Celtic were "intimately connected" and the senior club was "vicariously liable" for assaults carried out.
The litigation relates to historical claims of sexual assault by convicted paedophiles Jim Torbett - the founder of the Boys Club - and Frank Cairney, a former coach.
Laura Connor, from Thompsons Solicitors, said the firm's clients had wanted their voices to be heard.
"This litigation has been made far more complex and lengthy by the defender, while our clients have acted with resolute dignity throughout," she said.
"At long last they have achieved success and can take this compensation as confirmation that Celtic Boys Club was indeed inextricably linked to Celtic Football Club."
