Copolymers based on ethylene brassylate (EB) and δ-hexalactone (δ-HL), two monomers obtained from renewable sources, were synthesized with triphenyl bismuth by ring-opening polymerization. The poly(EB-co-δ-HL), with EB molar contents ranging from 49 to 90%, presented a slight deviation from the random distribution of sequences (R > 0.71) while WAXS measurements proved that only the EB blocks were able to crystallize (with crystallinity degrees of ∼23–39%). The low T_gs (<−27 °C), their reduced crystallization capability and melting temperatures from 50 to 65 °C make these thermoplastic elastomers (of good thermal stability) very easy to process. Likewise, their thermal properties led to mechanical behaviour with improved flexibility in comparison to poly(ε-caprolactone) or poly(ω-pentadecalactone) (elastic modulus between 57–274 MPa with high elongation at break values) at both 21 °C and 37 °C. On the other hand, the incorporation of δ-HL in addition to increase the amorphous character, brought a more disordered chain microstructure distribution, resulting in higher degradation rates in the range of 0.0028–0.0041 per day. Finally, metabolic activity and cell morphology studies using human dermal fibroblasts (HDFs) demonstrated that these materials are not cytotoxic and provide a valid substrate for cells to attach and proliferate, meaning that they are suitable for use in the biomedical field.