Biodegradable polymers have recently become popular; in particular, blends of poly(lactic acid) (PLA) and poly(butylene adipate terephthalate) (PBAT) have recently attracted significant attention due to their potential application in the packaging field. However, there is little information about the thermomechanical properties of these blends and especially the effect induced by the addition of PBAT on the shape memory properties of PLA. This work, therefore, aims at producing and investigating the microstructural, thermomechanical and shape memory properties of PLA/PBAT blends prepared by melt compounding. More specifically, PLA and PBAT were melt-blended in a wide range of relative concentrations (from 85/15 to 25/75 wt%). A microstructural investigation was carried out, evidencing the immiscibility and the low interfacial adhesion between the PLA and PBAT phases. The immiscibility was also confirmed by differential scanning calorimetry (DSC). A thermogravimetric analysis (TGA) revealed that the addition of PBAT slightly improved the thermal stability of PLA. The stiffness and strength of the blends decreased with the PBAT amount, while the elongation at break remained comparable to that of neat PLA up to a PBAT content of 45 wt%, while a significant increment in ductility was observed only for higher PBAT concentrations. The shape memory performance of PLA was impaired by the addition of PBAT, probably due to the low interfacial adhesion observed in the blends. These results constitute a basis for future research on these innovative biodegradable polymer blends, and their physical properties might be further enhanced by adding suitable compatibilizers.