The accelerating global demand for cobalt, driven primarily by lithium-ion batteries, has intensified the search for alternative sources of supply. Mine tailings represent a promising secondary resource, particularly in regions with extensive mining histories such as Chile. This study evaluates cobalt leaching from copper tailings using a deep eutectic solvent (DES), choline chloride–citric acid (ChCl–CA), with controlled addition of hydrogen peroxide. The tailings were subjected to pretreatments (froth flotation, chlorination, and thermal roasting) and then leached with choline chloride–citric acid-based DES or H₂SO₄. Temperature, leaching time, and solid–liquid ratio were evaluated. Results show that roasting significantly enhanced cobalt recovery when followed by citric acid or DES leaching, reaching up to 100% Co recovery. Under optimized conditions, DES-based leaching was effective and selective in a polymetallic matrix and achieved recoveries comparable to or better than acid leaching without generating toxic emissions. Although flotation and chlorination had limited effects on overall recovery, the results demonstrate the viability of integrated and cleaner technologies for valorizing tailings that contain critical metals such as cobalt.