This research work is focused on the synthesis, characterization, and application of cost-effective biochar–biopolymeric hybrid adsorbents from waste agricultural biomass and sodium alginate. The adsorbents were characterized by BET (Brunauer–Emmett–Teller), FTIR (Fourier transform infrared), XRD (X-ray diffraction), FESEM (field emission scanning electron microscopy), and bulk density measurement. The performance of the synthesized hybrid adsorbents has been tested for the removal of aqueous phase Ni2+ and Cu2+ metal ions at a concentration range of 25 to 100 mg/L, adsorbent dose of 1–3 g/L, and system temperature of 298–308 K, respectively. The effect of various physicochemical process parameters such as solution pH, adsorbent dose, initial metal ion concentration, temperature, and presence of salts on metal ion adsorption has been studied here, and experimental process parameters are being optimized by response surface methodology (RSM). The model was fitted well with the experimental data. Various kinetic models, namely, pseudo-first-order, pseudo-second-order, and Weber–Morris, have been fitted with batch experimental data, and the mechanism of adsorption has been identified. The maximum Langmuir monolayer adsorption capacity for Cu2+ and Ni2+ were 112 and 156 mg/g, respectively, which are comparative to other published adsorbent’s capacity data under similar experimental conditions. Thermodynamic parameter studies showed that the system was endothermic and spontaneous in nature.