Significant interest is devoted to the development of new polymer blends by using concepts of the circular economy. Such materials have predetermined properties, are easy to recycle, ecological, and have a low carbon footprint. This research presents obtaining and characterization of polymer blends based on low-density polyethylene (LDPE) and thermoplastic starch (TPS). In the first stage, TPS was obtained through the gelatinization process, and, in the second stage, mixtures of LDPE and TPS were obtained through a melt mixing process at 150 °C for 7 min. The physical–mechanical characteristics of the samples, like hardness, elongation at break, rebound resilience, and tensile strength, were determined. The sample containing maleic anhydride grafted low-density polyethylene (LDPE-g-MA) as a compatibilizer shows improvements in elongation at break and tensile strength (by 6.59% and 40.47%, respectively) compared to the test sample. The FTIR microscopy maps show that samples containing LDPE-g-MA are more homogeneous. The SEM micrographs indicate that TPS-s is homogeneously dispersed as droplets in the LDPE matrix. From the thermal analysis, it was observed that both the degree of crystallinity and the mass loss at high temperature are influenced by the composition of the samples. The melt flow index has adequate values, indicating good processability of the samples by specific methods (such as extrusion or injection).