Since the remarkable discovery of polyurethanes (PU), significant progress has been made in their synthesis and processing, expanding their applications across various fields. However, the inclusion of isocyanates and the utilization of toxic catalysts for PU synthesis impose a significant challenge for their biomedical application. In this study, we present a novel approach: an isocyanate and catalyst-free melt polycondensation process for the preparation of a series of poly(ester urethanes). To synthesize the poly(ester urethanes), we have employed a combination of poly(ethylene terephthalate) (PET) waste-derived monomers and a diverse range of renewable resources, including oleic acid, ethylene carbonate, citric acid, sebacic acid, and mannitol. The synthesis of the poly(ester urethanes) was confirmed by FTIR spectroscopy and 1 H NMR spectroscopy, while the physicochemical properties of the poly(ester urethanes) were investigated using XRD, TGA, DSC, and UTM. The thermal characteristics, mechanical properties, and biodegradation behavior of the poly(ester urethanes) can be adjusted by simply changing the PET waste-derived diols. The mechanical characteristics of the synthesized poly(ester urethanes) closely resemble those of various soft tissues found in the human body, including articular cartilage, cervical spinal components, ligaments, aorta, and soft collagenous bone, indicating its promising potential for soft tissue engineering applications. In addition to that, the synthesized poly(ester urethanes) exhibited excellent shape memory behavior, along with a good recovery response at ambient temperature. Furthermore, the synthesized poly(ester urethanes) demonstrated certain levels of antimicrobial activity, exceptional in vitro cytocompatibility, and cell proliferation against mouse fibroblast cells (NIH/3T3) as confirmed by alamar blue and live/dead assays suggesting its potential soft tissue engineering applications.