The aim of this work was to synthesize carboxymethyl cellulose (CMC) and produce CMC films from the cellulose of palm bunch and bagasse agricultural waste. The effect of various amounts of H2O2 (0–40% v/v) during delignification on the properties of cellulose, CMC, and CMC films was studied. As the H2O2 content increased, yield and the lignin content of the cellulose from palm bunch and bagasse decreased, whereas lightness (L*) and whiteness index (WI) increased. FTIR confirmed the substitution of a carboxymethyl group on the cellulose structure. A higher degree of substitution of CMC from both sources was found when 20%–30% H2O2 was employed. The trend in the L* and WI values of each CMC and CMC film was related to those values in their respective cellulose. Bleaching each cellulose with 20% H2O2 provided the cellulose with the highest viscosity and the CMC films with the greatest mechanical (higher tensile strength and elongation at break) and soluble attributes, but the lowest water vapor barrier. This evidence indicates that cellulose delignification with H2O2 has a strong effect on the appearance and physical properties of both CMCs.