Agri-food industries generate a large amount of waste that offers great revalorization opportunities within the circular economy framework. In recent years, new methodologies for the extraction of compounds with more eco-friendly solvents have been developed, such as the case of natural deep eutectic solvents (NADES). In this study, a methodology for extracting phenolic compounds from olive tree leaves using NADES has been optimized. The conditions established as the optimal rely on a solvent composed of choline chloride and glycerol at a molar ratio of 1:5 with 30% water. The extraction was carried out at 80 °C for 2 h with constant agitation. The extracts obtained have been analyzed by high-performance liquid chromatography coupled to tandem mass spectrometry (HPLC-MS/MS) in MRM mode. The comparison with conventional ethanol/water extraction has shown that NADES, a more environmentally friendly alternative, has improved extraction efficiency. The main polyphenols identified in the NADES extract were Luteolin-7-O-glucoside, Oleuropein, 3-Hydroxytyrosol, Rutin, and Luteolin at the concentrations of 262, 173, 129, 34, and 29 mg kg−1fresh weight, respectively.