Evidence from 23 witnesses details how ex-chief scout Eddie Heath, who died in 1983, groomed and abused young boys aged between 10 and 17 in the 1970s.
An external review said some adults at Chelsea must have been aware of Heath's abuse but "turned a blind eye".
In a statement, Chelsea's board apologised "unreservedly".
The report - led by barrister Charles Geekie QC - is also heavily critical of former assistant manager Dario Gradi, who is accused of failing to tell more senior club staff about an allegation regarding the sexual conduct of Heath, brought to him by the parent of a young player.
Gradi's alleged failure to report the claim "was a lost opportunity to expose Heath and prevent further abuse".
The BBC has approached 78-year-old Gradi for comment. In his evidence to the review, he denied trying to "smooth over" the matter in a meeting with the boy's father. He also said he reported the allegations to the club's assistant manager.
Meanwhile, a separate review into allegations of racial abuse from 1982 up until the late 1990s conducted by charity Barnado's concluded that "black players were subjected to a daily tirade of racial abuse".
More about: Chelsea