This work studied biocomposites based on a blend of low-density polyethylene (LDPE) and the ethylene–vinyl acetate copolymer (EVA), filled with 30 wt.% of cellulosic components (microcrystalline cellulose or wood flour). The LDPE/EVA ratio varied from 0 to 100%. It was shown that the addition of EVA to LDPE increased the elasticity of biocomposites. The elongation at break for filled biocomposites increased from 9% to 317% for microcrystalline cellulose and from 9% to 120% for wood flour (with an increase in the EVA content in the matrix from 0 to 50%). The biodegradability of biocomposites was assessed both in laboratory conditions and in open landfill conditions. The EVA content in the matrix also affects the rate of the biodegradation of biocomposites, with an increase in the proportion of the copolymer in the polymer matrix corresponding to increased rates of biodegradation. Biodegradation was confirmed gravimetrically by weight loss, an X-ray diffraction analysis, and the change in color of the samples after exposition in soil media. The prepared biocomposites have a high potential for implementation due to the optimal combination of consumer properties.