Atlantic salmon is rich in bioactive proteins, antioxidants, vitamins, and omega-3 fatty acids, making it a rich source of essential nutrients. However, it is highly susceptible to biochemical, physicochemical, and microbial spoilage. The aim of this study was to use natural oregano and dill antioxidant extracts in combination with modified atmosphere packaging (MAP) (CO2:N2 60:40) to retain the quality and delay lipid oxidation in Atlantic salmon (Salmo salar) during storage. Extract-treated samples and controls (both vacuum packed and in MAP) were stored under chilled conditions (4 ± 1 °C) for 0–16 days. Quality changes during storage were assessed in terms of drip loss, microbial growth, color, pH, protein solubility, and lipid oxidation. Primary and secondary lipid oxidation products were determined by means of peroxide value and TBARS. In parallel, volatile compounds were analyzed using GC-MS, SIFT-MS and SESI-MS. GC-MS indicated 29 recognizable VOCs present in the headspace of the salmon samples. SIFT-MS quantification was carried out for ammonia and 33 VOCs, including alcohols, several aldehydes, carboxylic acids, sulfur compounds, trimethylamine, and ammonia. While dill or oregano treatment reduced lipid oxidation after 16 days of storage, it did not affect VOC concentrations significantly. The study has revealed that changes of the measured concentration of volatiles with storage time could be used to monitor freshness and spoilage of the fish while observing the effect of natural antioxidants.