The club added an independent investigation had also revealed "serious allegations of child sex abuse" against another former junior coach, John Broome, whose alleged victims will also be eligible for compensation under the scheme.
Broome, who worked with City from 1964-71, died in 2010.
City did not reveal financial details of the scheme, but British media, including the BBC, reported on Monday that the club were set to offer millions of pounds in compensation.
Victims of the most serious crimes will receive six-figure sums in damages while those abused will also receive a personal apology from a senior club official, the BBC reported.
"The club reiterates ... its heartfelt sympathy to all victims for the unimaginably traumatic experiences that they endured," City said in a statement on its official website .
"All victims were entitled to expect full protection from the kind of harm they suffered as a result of their sexual abuse as children."
(Reporting by Simon Jennings in Bengaluru; Editing by Greg Stutchbury)
