The possibility of enriching the oil produced from Leccino cultivar olive fruits with phenolic and volatile compounds by adding olive leaves (2.5%) during industrial-scale production were investigated. Furthermore, the influence of the addition of leaves on the oil quality, composition, and oxidative stability during storage for 6 and 12 months was studied. A slight negative impact on the oil quality after processing with leaves was determined. The addition of leaves had no influence on the total saturated, monounsaturated, and polyunsaturated fatty acids in oils, while it influenced increases in total phenolic compounds (+29.55%), total secoiridoids (+29.43%), chlorophylls (+47.59%), and the oil stability index (+18.70%), and their higher values were also determined in the stored oils. The addition of leaves increased C5 volatiles (+10.50%) but decreased C6 volatiles (−10.48%). The intensity of most of the positive sensory characteristics increased in fresh oils obtained with leaves, and the established improvements were also maintained in the stored oils. The extractability of olive paste was positively affected by the addition of olive leaves, which increased the oil yield (+27.17%). The obtained results significantly contribute to the knowledge about the possibilities of enriching olive oils with bioactive compounds.