Tracing methods of non-European EVOOs commercialized worldwide are becoming crucial for effective authenticity controls. Limited analytical studies of these oils are available on a global scale, similar to those of European EVOOs. We report for the first time the fatty acid concentrations, bulk-oil 2H/1H, 13C/12C, and 18O/16O ratios and fatty acid 13C/12C ratios of 43 authentic monovarietal EVOOs from different geographical regions in Argentina and Uruguay. The samples were obtained from a wide range of latitudes and altitudes along an E–W profile, from lowlands near the Atlantic Ocean to the pre-Andean highlands near the Pacific Ocean. Principal component scores were used to cluster EVOOs into three groups— central-western Argentina, central Argentina, and Uruguay—based on nine stable isotope ratios and the oleic-linoleic acid concentration ratio. The bulk 2H/1H and 18O/16O values and 13C/12C of palmitoleic and linoleic acids provide good tools for differentiating these oils via linear discriminant analysis.