The Mediterranean diet well known for its beneficial health effects, including mood enhancement, is characterised by the relatively high consumption of extra virgin olive oil (EVOO), which is rich in bioactive phenolic compounds. Over 200 phenolic compounds have been associated with Olea europaea, and of these, only a relatively small fraction have been characterised. Utilising the OliveNetTM library, phenolic compounds were investigated as potential inhibitors of the epigenetic modifier lysine-specific demethylase 1 (LSD1). Furthermore, the compounds were screened for inhibition of the structurally similar monoamine oxidases (MAOs) which are directly implicated in the pathophysiology of depression. Molecular docking highlighted that olive phenolics interact with the active site of LSD1 and MAOs. Protein–peptide docking was also performed to evaluate the interaction of the histone H3 peptide with LSD1, in the presence of ligands bound to the substrate-binding cavity. To validate the in silico studies, the inhibitory activity of phenolic compounds was compared to the clinically approved inhibitor tranylcypromine. Our findings indicate that olive phenolics inhibit LSD1 and the MAOs in vitro. Using a cell culture model system with corticosteroid-stimulated human BJ fibroblast cells, the results demonstrate the attenuation of dexamethasone- and hydrocortisone-induced MAO activity by phenolic compounds. The findings were further corroborated using human embryonic stem cell (hESC)-derived neurons stimulated with all-trans retinoic acid. Overall, the results indicate the inhibition of flavin adenine dinucleotide (FAD)-dependent amine oxidases by olive phenolics. More generally, our findings further support at least a partial mechanism accounting for the antidepressant effects associated with EVOO and the Mediterranean diet.