From Longman Dictionary of Contemporary Englishfess up American English informalADMITto admit that you have done something wrong, although it is not very serious syn own upCome on, fess up! Who ate that last cookie? →fess→ See Verb table
Examples from the Corpus
fess up• Come on, fess up - you must have been the one who told her because no-one else knew!• If none of you guys fesses up, you're all grounded for a week.