Poly(butylene adipate-co-terephthalate) (PBAT) is a biodegradable polyester with excellent flexibility, while the low rigidity and gas barrier performance limits its further applications. In this work, a series of PBAT/polyglycolic acid (PGA) blends with and without reactive compatibilizers (ESO and ADR) were prepared by a twin-screw extruder. The thermal, rheological, morphological, mechanical, gas barrier, and biodegradable properties of the PBAT/PGA blends were studied in detail. It was found that the PBAT/PGA30 blend showed a noticeably worse tensile strength and breaking elongation compared to those of neat PBAT due to the poor miscibility between the two components. Compared with neat PBAT and the PBAT/PGA30 blend, the PBAT/PGA30/ESO/ADR blend exhibited a better stiffness–ductility balance with a tensile strength of 19.8 MPa, an elastic modulus of 529 MPa, and an elongation at break of 146%, which could be ascribed to the improvement of the compatibility between PBAT and PGA in the presence of ESO and ADR, reflecting the smaller size of the PGA phase dispersed in a PBAT matrix as observed by scanning electron microscopy. In addition, the gas barrier properties and biodegradability of the PBAT/PGA30/ESO/ADR blend were much better than those of neat PBAT, and they were further improved with an increase in PGA content. This work provides an effective method for the reinforcement of PBAT and opens up the possibility for its large-scale application in food packaging.