Acid oils (AO) are fat by-products of edible oil refining with a high energetic value, being an interesting option for a more sustainable aquaculture nutrition. This study was conducted to evaluate the effects of the partial replacement of fish oil (FO) in diets by two AO instead of crude vegetable oils on the lipid composition, lipid oxidation and quality of fresh European seabass fillets, and after their commercial refrigerated storage for 6 days. Fish were fed with five different diets, the added fat being FO (100%) or a blend of FO (25%) and another fat (75%): crude soybean oil (SO), soybean-sunflower acid oil (SAO), crude olive pomace oil (OPO), or olive pomace acid oil (OPAO). Fresh and refrigerated fillets were assessed for fatty acid profile, tocopherol (T) and tocotrienol (T3) composition, lipid oxidative stability, 2-thiobarbituric acid (TBA) value, volatile compound content, color, and sensory acceptance. Refrigerated storage did not affect T + T3 total content but increased secondary oxidation products (TBA values and volatile compound contents) in fillets from all diets. The FO substitution decreased EPA and DHA and increased T and T3 in fish fillets, but the recommended human daily intake of EPA plus DHA could still be covered with 100 g of fish fillets. Both a higher oxidative stability and a lower TBA value were found in SO, SAO, OPO, or OPAO fillets, obtaining the greatest oxidative stability in OPO and OPAO fillets. Sensory acceptance was not affected by the diet or the refrigerated storage, while the differences found in color parameters would not be perceived by the human eye. According to the oxidative stability and acceptability of flesh, SAO and OPAO are adequate replacements of FO as energy source in European seabass diets, which implies that these by-products can be upcycled, improving the environmental and economical sustainability of aquaculture production.