The extraction of phenolic compounds from olive leaves was optimized using three glycerol-based deep eutectic solvents (DESs) with lysine, proline, and arginine. A three-level Box–Behnken design was used to examine the influence of the liquid/solid ratio, concentration of DESs, and extraction temperature on the yield of the extraction process. A second-order polynomial model was used for predicting the polyphenol extraction yield. The optimal predicted conditions were used for extractions and they provided the highest total phenol yields with the glycerol–lysine exhibiting the best performance. Quantification of tyrosol, hydroxytyrosol, oleuropein, luteolin-7-O-glucoside, and rutin in the extracts showed high content in tyrosol in all DESs, particularly with glycerol–lysine and relatively similar contents with other studies for the other phenolic compounds. Finally, a linear relationship between tyrosol content and the total phenolic content of the extracts was observed.