Polyphenols have gained increasing attention for their therapeutic potential, particularly in conditions like cancer, due to their established antioxidant and anti-inflammatory properties. Recent research highlights their ability to bind to transition metals, such as copper. This is particularly noteworthy given the key role of copper both in the initiation and progression of cancer. Copper can modulate the activity of kinases required for the epithelial–mesenchymal transition (EMT), a process fundamental to tumor cell dissemination. We have previously demonstrated the copper-binding capacity of oleuropein, a secoiridoid found in Olea europaea. In the present study, we investigated the effect of hydroxytyrosol, the primary oleuropein metabolite, on the metastatic potential of three triple-negative breast cancer cell lines (MDA-MB-231, MDA-MB-468, and SUM159). We found that hydroxytyrosol modulated the intracellular copper levels, influencing both the epithelial and mesenchymal markers, by downregulating copper-dependent AKT phosphorylation, a member of the EMT signaling cascade, through Western blot, RT-qPCR, and immunofluorescence. Indeed, by optical spectra, EPR, and in silico approaches, we found that hydroxytyrosol formed a complex with copper, acting as a chelating agent, thus regulating its homeostasis and affecting the copper-dependent signaling cascades. While our results bring to light the copper-chelating properties of hydroxytyrosol capable of countering tumor progression, they also provide further confirmation of the key role of copper in promoting the aggressiveness of triple-negative breast cancer cells.