A new family of polyester-based copolymers-poly(sorbitol adipate-co-ethylene glycol adipate) (PSAEG), poly(sorbitol adipate-co-1,4 butane diol adipate) (PSABD), and poly (sorbitol adipate-co-1,6 hexane diol adipate) (PSAHD)-was obtained with a catalyst-free melt polycondensation procedure using the multifunctional non-toxic monomer sorbitol, adipic acid, and diol, which are acceptable to the human metabolism. Synthesized polyesters were characterized by FTIR and 1H NMR spectroscopy. The molecular weight and thermal properties of the polymers were determined by MALDI mass spectroscopy, differential scanning calorimetry (DSC), and thermogravimetric analysis. The degradation rate was investigated, at 37 °C, in 0.1M NaOH (pH 13) and in phosphate-buffered solution (PBS) at pH 7.4. It was found that the polymers degraded faster in NaOH (i.e., in a day) compared to their degradation in PBS, which was much slower (in a week). The highest degradation rate was noticed for the PSAEG sample in both media, whereas PSAHD was the most stable polymer at pH 7.4 and 13. A reduced hydrophilicity of the polymers with diol length was indicated by low swelling percentage and sol content in water and DMSO. Mechanical studies prove that all the polymers are elastomers whose flexibility increases with diol length, shown by the increase in percentage of elongation at break and the decrease in tensile stress and Young's modulus. These biodegradable copolymers with adaptable physicochemical characteristics might be useful for a broad variety of biological applications by merely varying the length of the diol.