Fabrication of the conductive copper structures on the surface of various dielectric materials is quite important in many fields of science. There are a lot of chemical and physical methods and approaches that can be used for this purpose. Recently, we demonstrated the possibility of performing laser-assisted deposition of copper using deep eutectic solvents (DESs). The use of DESs instead of aqueous solutions allowed increasing the deposition rate by more than 100 times. In this work, for the first time, the influence of different chemical parameters, such as nature of deep eutectic solvent and concentration of copper, as well as physical parameters, including the intensity of laser radiation and the scanning speed, on the process of copper deposition was investigated. We experimentally showed and confirmed theoretically that the use of citric and tartaric acids such as DES components provides conditions for the formation of copper micropatterns with predefined characteristics.