The use of bioplastic mulch in agriculture has increased dramatically in the last years throughout the world. Nowadays, biodegradable materials for mulching films strive to constitute a reliable and more sustainable alternative to classical materials such as polyethylene (PE). The main challenge is to improve their durability in the soil to meet the required service length for crop farming by using benign and sustainable antioxidant systems. Here, we report the design and fabrication of biodegradable materials based on polybutylene (succinate adipate) (PBSA) for mulching applications, incorporating a fully biobased polymeric antioxidant deriving from ferulic acid, which can be extracted from an industrial by-product. Poly-dihydro (ethylene ferulate) (PHEF) from ferulic acid was synthesized by a two-step polymerization process. It is characterized by improved thermal stability in comparison with ferulic acid monomer and therefore suitable for common industrial processing conditions. Different blends of PBSA and PHEF obtained by melt mixing or by reactive extrusion were prepared and analyzed to understand the effect of the presence of PHEF. The results demonstrate that PHEF, when processed by reactive extrusion, presents a remarkable antioxidant effect, even in comparison with commercial additives, preserving a high level of the mechanical properties of the PBSA matrix without affecting the biodegradable character of the blend.