In this study, we show the possibilities of developing a method for manufacturing electrically conductive copper patterns of arbitrary topology on various dielectric substrates by laser-induced synthesis from deep eutectic solvents. The possibility of printing on the industrially demanded dielectrics is shown, e.g., on polyimide, fiberglass plastic, and polytetrafluoroethylene (PTFE) substrates. The geometric and electrical properties of the resulting structures, as well as their composition, have been studied. The influence of the substrate material is shown to be substantial for the effective rate of formation of structures and their final properties.