Celtic Football Club has expressed "deep regret" over the abuse carried out by paedophile Jim Torbett.
The Celtic Boys Club founder was jailed for six years after being found guilty of sexually abusing three boys.
The club had been criticised for its silence following Torbett's conviction at the High Court in Glasgow on Monday.
On Wednesday, Celtic said it had taken the allegations of abuse "extremely seriously" because of its "historic contacts" with Celtic Boys' Club.
The club published the statement on its website.
It said: "Celtic Football Club wishes to express our deep regret that the incidents took place and sympathy for the victims who suffered abuse.
"We are grateful for the courage of those who have come forward to report abuse and to give evidence after such a long period of time.
"We have great respect for them and their families as they continue to cope with the distressing effects of the abuse they suffered."
Torbett, of Kelvindale, Glasgow, founded Celtic Boys Club in 1966.
The ex-football coach was jailed for two years after being found guilty of shameless indecency in November 1998.
Justice then caught up with Torbett for a second time after an investigation by BBC journalists Mark Daly and Calum McKay.
On Monday, he was found guilty of abusing three boys between August 1986 and August 1994.
Following his conviction, Celtic was criticised for its failure to comment on the case.
One of his victims, Kenny Campbell, said he wanted an apology from the club.
In the statement issued on Wednesday, the club said allegations regarding abuse at Celtic Boys' Club had first emerged in the 1990s.
It continued: "Although Celtic Football Club is an entirely separate organisation, we have always taken these allegations extremely seriously because of our historic contacts with Celtic Boys' Club.
"All investigations by the police and other inquiries were given our full support. We encouraged any individuals involved to report all information to the police so that matters could be investigated fully.
"Celtic Football Club continues to encourage any victim of abuse to report these crimes to the police."
The club said it took steps to develop a new code of conduct and procedures to protect young people and became the first club in Scotland to appoint a safeguarding officer.
The statement concludes: "The abuse of children is an issue affecting many areas of society, including a large number of football clubs, sports clubs, youth organisations, educational institutions and religious bodies across Britain.
"Celtic Football Club strongly believes that children and young people involved in football have the right to protection from all forms of harm and abuse and is committed to ensuring this and to promoting their wellbeing through continued cooperation with our children and young people, parents and carers and the relevant authorities."
Celtic manager Brendan Rodgers said he was unable to elaborate on the club's statement.
But speaking ahead of Thursday's Europa League match against RB Leipzig, Rodgers expressed "empathy and sympathy" for the victims of such crimes.
Boys Club rebranded
Celtic Boys Club has been rebranded as St Patrick's Sports Academy, BBC Scotland has learned.
The team's name, logo and green and white hooped shirts were changed in August.
The academy did not respond to a request for a comment about the timing and reason behind the move.
Its teams now play in a different style of green and white strip, featuring a new crest which states the club was established in 2018.
The academy runs its own official social media accounts but the under-18s team still maintains a separate Facebook page.
Earlier posts on the account show that results from last season were listed under "Celtic BC", and details in the "about" section still reference Celtic Boys Club.
The academy, which is based in Motherwell, North Lanarkshire, has 10 youth teams.
It also runs a Soccer School, aimed at three to five year olds, as well as walking, running and cycling groups.
The boys club no longer has an official presence on social media and its main Facebook and Twitter accounts have been deleted.