Poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) is a very promising biodegradable copolyester of high interest in food packaging. Its inherent brittleness and narrow processing window make it necessary to blend it with flexible biopolyesters, such as poly(butylene succinate-co-adipate) (PBSA). However, the resultant biopolyester blends are thermodynamically immiscible, which impairs their performance and limits their applications. This study is the first to explore the use of poly(butylene succinate-co-adipate) grafted with maleic anhydride (PBS-g-MAH) as a novel reactive additive to compatibilize PHBV/PBSA blends. The compatibilizer was prepared by a reactive melt-mixing process of PBSA and maleic anhydride (MAH) using dicumyl peroxide (DCP) as an organic radical initiator, achieving a grafting degree (G_d) of 5.4%. Biopolyester blend films were thereafter prepared via cast extrusion and their morphological, thermal, mechanical, and barrier properties were characterized. Compatibilization by PBSA-g-MAH was confirmed by observing an improved phase interaction and lower dispersed domain sizes in the blends with 15 wt% PBSA. These compatibilized PHBV/PBSA blends were thermally stable up to 285 °C, showed enhanced ductility and toughness, as well as providing an improved barrier against water and limonene vapors and oxygen. These findings suggest that the use of MAH-grafted biopolyesters can represent an effective strategy to improve the properties of biopolyester blends and open up new opportunities for the application of PHBV-based formulations for food packaging.