The valorization of wastes generated in the processing of farmed fish is currently an issue of extreme relevance for the industry, aiming to accomplish the objectives of circular bioeconomy. In the present report, turbot (Scophthalmus maximus) by-products were subjected to Alcalase hydrolysis under the optimal conditions initially defined by response surface methodology. All the fish protein hydrolysates (FPHs) showed a high yield of digestion (>83%), very remarkable degrees of hydrolysis (30−37%), high content of soluble protein (>62 g/L), an excellent profile of amino acids, and almost total in vitro digestibility (higher than 92%). Antioxidant and antihypertensive activities were analyzed in all cases, viscera hydrolysates being the most active. The range of average molecular weights (Mw) of turbot hydrolysates varied from 1200 to 1669 Da, and peptide size distribution showed that the hydrolysate of viscera had the highest content of peptides above 1000 Da and below 200 Da.