Quantum-chemical calculations of the acidity indices of Cu(II) aqua ions were performed using the B3LYP, PBE0 and w-B97XD functionals in combination with the 6-311++G(d,p), aug-cc-pVDZ and def2-TZVP atomic basis sets. In the molecular-continuum model, the Cu(H2O)182+ aqua complex (6 H2O molecules in the first and 12 molecules in the second hydration sphere) was considered as a reference Cu(II) aqua ion. Its interaction with the dielectric environment in the solution was taken into account in the polarized continuum model. In the initial aqua complex, a proton was sequentially removed, and the resulting Cu(II) aquahydroxocomplexes were subjected to complete geometry optimization. The Gibbs free energies of ionization processes were calculated as the difference between the total Gibbs energies of the reaction products and the initial reagents. Free energies for intermediate aquahydroxocomplexes were obtained from thermochemical analysis, and for the proton in an aqueous solution H+(aq), the free energy was calculated by a special aproach using the experimental Gibbs energy of hydration. Analysis of the calculation results showed that the B3LYP/aug-cc-pVDZ and w-B97XD/aug-cc-pVDZ combinations provide satisfactory agreement with the experimental values for all four stages of ionization (hydrolysis) of Cu(II) aqua ions. Based on this, it can be concluded that these combinations of the density functional method and the atomic basis set can be recommended for calculating the formation constants of Cu(II) complexes in aqueous solutions. Along with this, it is noted that for the first stage of ionization of the Cu(II) aqua ion, from which the primary reconstruction of the aqua complex begins, satisfactory pKa1 values are achieved at almost all calculation levels. Therefore, other calculation levels used may also prove satisfactory for calculating the formation constants of Cu(II) complexes in aqueous solutions.