Framing the Circular Bioeconomy, the use of reactive compatibilizers was applied in order to increase the interfacial adhesion and, hence, the physical properties and applications of green composites based on biopolymers and food waste derived lignocellulosic fillers. In this study, poly(butylene succinate) grafted with maleic anhydride (PBS-g-MAH) was successfully synthetized by a reactive melt-mixing process using poly(butylene succinate) (PBS) and maleic anhydride (MAH) that was induced with dicumyl peroxide (DCP) as a radical initiator and based on the formation of macroradicals derived from the hydrogen abstraction of the biopolymer backbone. Then, PBS-g-MAH was used as reactive compatibilizer for PBS filled with different contents of pistachio shell flour (PSF) during melt extrusion. As confirmed by Fourier transform infrared (FTIR), PBS-g-MAH acted as a bridge between the two composite phases since it was readily soluble in PBS and could successfully form new esters by reaction of its multiple MAH groups with the hydroxyl (−OH) groups present in cellulose or lignin of PSF and the end ones in PBS. The resultant compatibilized green composites were, thereafter, shaped by injection molding into 4-mm thick pieces with a wood-like color. Results showed significant increases in the mechanical and thermomechanical rigidity and hardness, meanwhile variations on the thermal stability were negligible. The enhancement observed was related to the good dispersion and the improved filler-matrix interfacial interactions achieved by PBS-g-MAH and also to the PSF nucleating effect that increased the PBS’s crystallinity. Furthermore, water uptake of the pieces progressively increased as a function of the filler content, whereas the disintegration in controlled compost soil was limited due to their large thickness.