Herein, we describe the batch and fixed-bed column adsorption of Cu2+ and Pb2+ by raw and treated date palm leaves (DP) and orange peel (OP) waste biomass. Contact time, pH, adsorbent dose, and particle size were optimized in batch adsorption experiments, while breakthrough curves obtained in fixed-bed adsorption experiments were used to determine the effects of bed height, initial metal concentration, particle size, and flow rate. The use of treated DP and/or OP in batch adsorption mode increased the removal efficiency of metal ions by 20–30% compared to that observed for raw adsorbents. The equilibration time was estimated as 0.5 h, with rapid metal removal observed during the first 15 min at an optimum pH value of ~5. Increasing the adsorbent dose from 0.5 to 6–7 g enhanced the metal removal efficiency by ~60%, whereas a particle size increase from 50 to 300 µm decreased this value by about 30% for both Cu2+ and Pb2+ and both raw and treated DP/OP. Both breakthrough and exhaust times increased with increasing bed height of the fixed-bed column, and the effect observed for treated DP exceeded that observed for raw DP by a factor of two. Conversely, both breakthrough and exhaust times decreased with increasing initial metal concentration, particle size, and flow rate. Increasing the particle size from 100–150 to 300 µm changed the exhaust time by 8 h when treated DP was used for Pb2+ adsorption. The obtained linear regression coefficients (R2 = 0.9–0.99) suggest that both Thomas and Yoon–Nelson models are well-suited for predicting the adsorption performance of the present system.