The pomegranate processing industry generates worldwide enormous amounts of by-products, such as pomegranate peels (PPs), which constitute a rich source of phenolic compounds. In this view, PPs could be exploited as a sustainable source of ellagic acid, which is a compound that possesses various biological actions. The present study aimed at the liberation of ellagic acid from its bound forms via ultrasound-assisted alkaline hydrolysis, which was optimized using response surface methodology. The effects of duration of sonication, solvent:solid ratio, and NaOH concentration on total phenol content (TPC), antioxidant activity, and punicalagin and ellagic acid content were investigated. Using the optimum hydrolysis conditions (i.e., 32 min, 1:48 v/w, 1.5 mol/L NaOH), the experimental responses were found to be TCP: 4230 ± 190 mg GAE/100 g dry PPs; AABTS: 32,398 ± 1817 µmol Trolox/100 g dry PPs; ACUPRAC: 29,816 ± 1955 µmol Trolox/100 g dry PPs; 59 ± 3 mg punicalagin/100 g dry PPs; and 1457 ± 71 mg ellagic acid/100 g dry PPs. LC-QTOF-MS and GC-MS analysis of the obtained PP extract revealed the presence of various phenolic compounds (e.g., ellagic acid), organic acids (e.g., citric acid), sugars (e.g., fructose) and amino acids (e.g., glycine). The proposed methodology could be of use for food, pharmaceutical, and cosmetics applications, thus reinforcing local economies.