The impact of the covering vegetable oil (sunflower oil, refined olive oil and extra virgin olive oil, EVOO) on the physicochemical and sensory profiles of canned tuna (Katsuwonus pelamis species) was evaluated, using analytical techniques and a sensory panel. The results showed that canned tuna covered with EVOO possesses a higher content of total phenols and an enhanced antioxidant capacity. This covering medium also increased the appreciated redness-yellowness color of the canned tuna, which showed a higher chromatic and intense color. Olfactory and kinesthetic sensations were significantly dependent on the type of oil used as covering medium. Tuna succulence and adhesiveness were promoted by the use of EVOO, which also contributed to decreasing the tuna-related aroma sensations. The tuna sensory data could be successfully used to identify the type of vegetable oil used. Moreover, a potentiometric electronic tongue allowed discriminating between the canned tuna samples according to the vegetable oil used (mean sensitivity of 96 ± 8%; repeated K-fold cross-validation) and the fruity intensity of the EVOO (mean sensitivity of 100%; repeated K-fold cross-validation). Thus, the taste sensor device could be a practical tool to verify the authenticity of the declared covering medium in canned tuna and to perceive the differences in consumers’ taste.