Modern membrane technologies are useful for enhancing the concentration of phenolic antioxidants in olive mill waste water (OMWW) to produce concentrates with valuable applications in functional foods. Three types of OMWW concentrates, each with different levels of solute concentration and purity, were obtained from a single OMWW batch and dissolved in two extra virgin olive oils to achieve saturated solutions. Three addition levels were considered. Accelerated aging testing of the oils was performed at 60 °C and the samples were analyzed after two, four, and 6 weeks of aging. D-optimal design was used to select the 26 experiments that allowed the evaluation of the influence of the different variables on oil stability. The addition of OMWW concentrates resulted in a significant increase in the Radical Scavenging Activity (RSA) of the olive oils. Under these mild experimental conditions, the moderate formation of fatty acid hydroperoxides was probably masked by interfering compounds.