Poly(glycerol sebacate) (PGS) has been explored extensively for tissue engineering applications due to its elastomeric mechanical properties and biocompatibility, but its relatively low mechanical strength and poor hydrophilicity restrict its practical applications in tissue engineering. In this study, we developed new biodegradable elastomeric copolyesters poly(glycerol-co-sebacic acid-co-L-lactic acid-co-polyethylene glycol) (PGSLP) by simultaneously introducing L-lactic acid (LLA) and polyethylene glycol (PEG) into the PGS network. The synthesized copolyesters were well-characterized to evaluate their physicochemical properties, mechanical strength and in vitro degradation properties, and their biocompatibility was also evaluated by a combination of in vivo and in vitro experiments. It is found that the PGSLP exhibited typical elastic properties, and possessed better hydrophilicity, water uptake capacity as well as improved degradation behaviors compared to PGS, which were beneficial for tissue engineering applications. More importantly, the physicochemical properties of PGSLP could be tuned in a wide range by changing the content of LLA and PEG, and their mechanical properties were visibly influenced by the curing conditions such as curing time. Furthermore, the L929 mouse fibroblast cells cultured on the PGSLP exhibited high viability, good spreading and proliferation, and PGSLP implants did not induce obvious inflammatory reaction but promoted neovascularization after subcutaneous implantation in Sprague-Dawley rats for 5 weeks. Hence, the developed PGSLP copolyesters may offer a much better choice of scaffolds than PGS for practical tissue engineering applications.