Two binuclear coordination compounds of Cu(II) chloride with the bitopic ligand 1,1,2,2-tetrakis(pyrazol-1-yl)ethane (Pz4) of the composition [Cu2(µ2-Pz4)(DMSO)2Cl4]·4H2O and [Cu2(µ2-Pz4)(DMSO)2Cl4]∙2DMSO were prepared and characterized by elemental analysis, IR spectroscopy, thermogravimetric analysis, single-crystal X-ray diffraction, and powder diffraction analysis. It was shown that in contrast to silver(I) and copper(II) nitrates, copper(II) chloride forms discrete complexes instead of coordination polymers. The supramolecular structure of the complex [Cu2(µ2-Pz4)(DMSO)2Cl4]·4H2O with lattice water molecules is formed by OH···Cl and OH···O hydrogen bonds. Density functional theory (DFT) calculations of vibrational frequencies of the ligand and its copper(II) complex allowed for assigning IR bands to specific vibrations.