A new hybrid catalyst consisting of cobalt nanoparticles immobilized onto cellulose was developed. The cellulosic matrix is derived from date palm biomass waste, which was oxidized by sodium periodate to yield dialdehyde and was further derivatized by grafting orthoaminophenol as a metal ion complexing agent. The new hybrid catalyst was characterized by FT-IR, solid-state NMR, XRD, SEM, TEM, ICP, and XPS. The catalytic potential of the nanocatalyst was then evaluated in the catalytic hydrogenation of 4-nitrophenol to 4-aminophenol under mild experimental conditions in aqueous medium in the presence of NaBH4 at room temperature. The reaction achieved complete conversion within a short period of 7 min. The rate constant was calculated to be K = 8.7 × 10−3 s−1. The catalyst was recycled for eight cycles. Furthermore, we explored the application of the same catalyst for the hydrogenation of cinnamaldehyde using dihydrogen under different reaction conditions. The results obtained were highly promising, exhibiting both high conversion and excellent selectivity in cinnamyl alcohol.