The authors agree that this surname and its variants have their origin in the ancient Greek árktos ("bear"), either directly or through dialectal modifications of the Greek spoken in Italy. F. Miranda specifies that this Greek is called Griko, and that the etymon may also appear as the Greek name arkoudi, with the same meaning. Both Miranda and E. Rossoni note that the surname could equally derive from the name of the Greek island of Arkoudi, located between Lefkada and Ithaca.

V. Blunda proposes a different reading: the etymon would be the Greek term arcydìa, "she-bear", that is, the female of the bear, in turn derived from árctos. According to Blunda, the term originally functioned as a nickname applied to a female ancestor for her corpulence or character, and later became a family surname. The variant Arcudi would reflect a graphic adaptation of the same etymon.

Rossoni documents the transformation into a surname from the 16th century with the theologian Petrus Arcudius, and in the 17th century with the bishop of Nusco —in the Avellino area— Francesco Arcudio. As for the geographical distribution, Miranda notes that it is an essentially Sicilian surname, spread mainly in the Messina area —in localities such as San Marco d'Alunzio, Tortorici and Naso—, and also present in the areas of Catania, Palermo and Enna.