Processing of fish in aquaculture generates considerable amounts of by-products that remain underused and/or unexploited. We evaluated the nutritive content of fish by-products (head, gills, intestines, trimmings, bones, and skin) from meagre and gilthead sea bream fish species reared in Greece in order to estimate their nutritional value for future development of high added-value products. The proximate composition of the fish samples (total protein, total lipid, ash, moisture, and macro-element content) was determined using the Association of Official Analytical Chemists (AOAC) and International Organization for Standardization (ISO) official methods. The content of fatty acids was determined using capillary gas chromatography, and the protein profile was estimated employing scientific orbitrap mass spectrophotometer methodology. The nutrient composition of fish by-products presented fluctuations among the different by-products. Skin was the most significant protein source, trimmings and bones were high in calcium, and the head, intestines, and bones were a good source of lipids. The most abundant lipid acids found in by-products were oleic, palmitic, linoleic, and eicosenoic acids, whereas the most abundant proteins were adenosine triphosphate (ATP) synthase subunit epsilon, mitochondrial nicotinamide adenine dinucleotide (NADH) dehydrogenase, and mitochondrial cytochrome b-c1 complex subunit 8. These data suggest that by-products constitute valuable sources of nutrients and could therefore be exploited in accordance with the principles of a circular economy.