Thompsons Solicitors is acting on behalf of around 30 former players amid a US-style class action lawsuit against Celtic Plc for damages.
The remaining eight are expected to be settled in the coming weeks, Thompsons Solicitors added.
Celtic had indicated back in September 2023 that they were seeking to settle the legal claims after a judge previously gave the go-ahead for group litigation to proceed.
The action relates to historical abuse at the youth club – which was not formally affiliated with Celtic FC – by convicted paedophiles James Torbett and Frank Cairney.
Torbett was the founder of the club, while Cairney was a former coach.
Laura Connor, partner and head of the life impact team at Thompsons Solicitors, said the firm’s clients had wanted their voices to be heard.
Speaking to Sky News’ Scotland correspondent Connor Gillies, Ms Connor said the settlements had been “decades in the making”.
She added: “For a number of years these cases have been defended and much of that has been made public – the approach taken by Celtic in distancing themselves from Celtic Boys Club.
“And that’s really been the main issue throughout these cases.
“There are convictions. We know that our clients were abused as they have told us.
“The cases have centred on us proving that Celtic were responsible for the boys’ club and the coaches at the boys’ club.
“Whilst there haven’t been any formal admissions in that respect, our clients can certainly take now that the compensation they have been awarded as a reflection of that relationship now being accepted.”
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Celtic Boys Club was established as a feeder team to the senior Celtic side in 1966.
Celtic repeatedly insisted they were a separate entity from the youth club, however, lawyers acting on behalf of the victims argued both were “intimately connected” as they shared players, kit, officials and premises.
Following a hearing at Scotland’s highest civil court, the Court of Session in Edinburgh, Lord Arthurson gave the go-ahead for the group action to proceed.
Group proceedings are similar to US class actions and were brought into law in Scotland in 2020.
Ms Connor described the compensation as a “significant moment”.
However, she noted: “I don’t think anyone is celebrating a successful outcome here because the compensation doesn’t change what has happened to them, or the impact of that, but hopefully it can be used positively now to move forward.”
Speaking about the length of time it has taken for Celtic to settle the claims, Ms Connor added: “I would say that from what I have seen, it has made the injuries worse because it has gone on for a number of years.
“They have felt as though they’ve not been believed, they’ve not been accepted, and that efforts have been made to avoid them as individuals being compensated.”
Celtic FC previously said they were “appalled by any form of historical abuse”.
The club have been contacted for further comment.
