We have shown that the adsorption of Cu2+ ions on various metal oxides, depending on the pH of the solution, can be described assuming the formation of only two surface complexes with surface hydroxyl groups SOH: SOCu(OH) and SOCu+. Using an ion-selective electrode for Cu2+, we determined the adsorption edges, i.e., the dependence of the amount of adsorbed metal expressed as a percentage depending on the solution pH for three oxides: TiO2, Al2O3, and SiO2. The measurements were carried out with high surface coverage where the ratio of the adsorption sites/copper ions in the system were from 2 to 3, depending on the oxide. Simultaneously, with the adsorption edge, the hydrogen surface charge density and the electrokinetic potential of the oxide particles were measured as a function of pH. These three types of experimental data were fitted all together using the surface complexation model (2-pK TLM). In modeling, it was not necessary to consider the precipitation of Cu(OH)2 on the oxide surface to obtain good agreement with the data. Additionally, it was shown that the presence of charged surface species SOCu+ (about 10% of total adsorbed copper) was crucial to fit the data for zeta potential.