Series of copolyesters based on poly(propylene succinate) (PPS) and poly(butylene succinate) (PBS), which can be produced from biological feedstock, and postconsumer poly(ethylene terephthalate) (PET) were synthesized with the aim of developing sustainable materials which combine the mechanical properties of high performance elastomers with those of flexible plastics. The aliphatic polyesters are synthesized by the catalyzed two-step transesterification reaction of dimethyl succinate (DMS), 1,3-propanediol (PD) and 1,4-butanediol (BD) followed by melt reaction with PET in bulk. The content of PET segments in the polymer chains was varied from about 10 to 100 wt% per 100wt% PPS or PBS. The effect of the introduction of the PET segments on the structure, thermal, physical and mechanical properties is investigated. The composition and structure of these aliphatic/aromatic copolyesters were determined by NMR spectroscopy. The thermal properties are investigated using differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). The level of crystallinity was studied by means of DSC and wide-angle X-ray scattering. A depression of melting temperature and a reduction of crystallinity of copolyesters with increasing content of PET segments were observed. Consequently, the tensile modulus and strength of copolyesters decrease, and the elongation at break increases with PET content in the range of 10−50 wt%. Thus, depending on PET content, the properties of copolyesters can be tuned ranging from semi-crystalline polymers possessing good tensile modulus (380 MPa) and strength (24 MPa) to nearly amorphous polymer of high elongation (∼800%), and therefore they may find applications in thermoplastics as well as elastomers or impact modifiers.