The Cincinnati Enquirer and WCPO-TV said the plea was entered to five counts of "failure to report a felony crime," all fourth-degree misdemeanors, for abuses occurring between 1978 and 1982. Each count carries a mandatory $2,000 fine.
The archdiocese waived a jury trial, allowing Judge Richard Niehaus to find the church guilty on all counts and order the maximum sentence: a $10,000 fine.
A guilty plea would have required the church to acknowledge wrongdoing, while a no-contest plea does not require such an admission.
The Most Rev. Daniel Pilarczyck, archbishop of Cincinnati, declined comment during the hearing.
Hamilton County Prosecutor Mike Allen said he would terminate his two-year-old investigation of the archdiocese, but charges might be pending against the four priests involved in the alleged abuse.
The Enquirer said the plea agreement is believed the first in the nation to require a diocese or a church official to plead to criminal charges related to sexual abuse.