Olive oil is one of the oldest and essential edible oils in the market. The classification of olive oils (e.g. extra virgin, virgin, refined) is often influenced by factors ranging from its complex inherent physiochemical properties (e.g. fatty acid profiles) to the undisclosed manufacturing processes. Therefore, olive oils have been the target of adulteration due to its profitable margin. In this work, we demonstrate that multi-parametric time-domain NMR relaxometry can be used to rapidly (in minutes) identify and classify olive oils in label-free and non-destructive manner. The subtle differences in molecular microenvironment of the olive oils induce substantial changes in the relaxation mechanism in the time-domain NMR regime. We demonstrated that the proposed NMR-relaxation based detection (AUC = 0.95) is far more sensitive and specific than the current gold-standards in the field i.e. near-infrared spectroscopy (AUC = 0.84) and Ultraviolet-visible spectroscopy (AUC = 0.73), respectively. We further show that, albeit the inherent complexity of olive plant natural phenotypic variations, the proposed NMR-relaxation based traits may be a viable mean (AUC = 0.71) in tracing the regions of origin for olive trees, in agreement with their geographical orientation.