The strong demand for rare-earth elements (REEs) is driven by their wide use in high-tech devices. New processes have to be developed for valorizing low-grade ores or alternative metal sources (such as wastes and spent materials). The present work contributed to the development of new sorbents for the recovery of rare earth ions from aqueous solutions. Functionalized mesoporous silica composite was synthesized by grafting diethylenetriamine onto composite support. The physical and chemical properties of the new sorbent are characterized using BET, TGA, elemental analysis, titration, FTIR, and XPS spectroscopies to identify the reactive groups (amine groups: 3.25 mmol N g−1 and 3.41 by EA and titration, respectively) and their mode of interaction with Nd(III) and Gd(III). The sorption capacity at the optimum pH (i.e., 4) reaches 0.9 mmol Nd g−1 and 1 mmol Gd g−1. Uptake kinetics are modeled by the pseudo-first-order rate equation (equilibrium time: 30–40 min). At pH close to 4–5, the sorbent shows high selectivity for rare-earth elements against alkali-earth elements. This selectivity is confirmed by the efficient recovery of REEs from acidic leachates of gibbsite ore. After elution (using 0.5 M HCl solutions), selective precipitation (using oxalate solutions), and calcination, pure rare earth oxides were obtained. The sorbent shows promising perspective due to its high and fast sorption properties for REEs, good recycling, and high selectivity.