The authors agree that the surname derives from the trade of maker of sieves. R. Brondolo specifies that the etymological base is the Latin cribrum, "sieve" or "screen", and that the surname designated those who exercised that trade.

Surnames in Italy notes that the oldest known document is a Milanese parchment of 1086, in which a Pietro son of Arderico qui dicitur Cribello appears. From there, the surname is recorded continuously in the history of Milan: an Uberto Crivelli was archbishop of Milan in 1186 and then pope under the name of Urban III. In the oath of fidelity to the Holy See of 1266 there figure eight bearers of the surname, and in the list of Milanese noble families of 1377 four differentiated branches are documented.

The presence of the surname in the institutional and economic life of Milan extends over several centuries: members are recorded in the Council of the Nine Hundred of the Golden Ambrosian Republic in 1447, in the court of the Sforza towards the end of the 15th century, and in the Register of the Wool Merchants between the 14th and 16th centuries. From the 17th century multiple feudal concessions to different branches of the family in territories of Lombardy are documented.