The efficiency of Cu(II) removal from aqueous solution by two adsorbents, silica SBA-15 and titanosilicate ETS-10, was investigated. Effects of various experimental parameters such as: contact time, pH, initial copper concentration, adsorbent dosage, temperature were investigated in order to determine the maximum adsorption capacity of the adsorbents. The maximum adsorption capacity of silica SBA-15 was achieved at pH 5.0, and of titanosilicate ETS-10 at pH 6.0. The Freundlich, Langmuir, and Temkin isotherm models were applied in order to describe the equilibrium adsorption of Cu(II) by the studied adsorbents. Equilibrium data fitted well to the Langmuir model with a higher adsorption capacity of ETS-10 (172.53 mg·g−1) towards Cu(II) than SBA-15 (52.71 mg·g−1). Pseudo-first- and pseudo-second-order, Elovich, and Weber–Morris intraparticle diffusion models were used for description of the experimental kinetic data. It was found that the pseudo-first-order and pseudo-second-order kinetic models were the best applicable models to describe the adsorption kinetic data. Thermodynamic parameters that characterize the process indicated that the adsorption of Cu(II) onto the two adsorbents is spontaneous and endothermic.