Developments of past years placed the bio-based polyesters as competitive substitutes for fossil-based polymers. Moreover, enzymatic polymerization using lipase catalysts has become an important green alternative to chemical polymerization for the synthesis of polyesters with biomedical applications, as several drawbacks related to the presence of traces of metal catalysts, toxicity and higher temperatures could be avoided. Copolymerization of ϵ-caprolactone (CL) with four hydroxy-fatty acids (HFA) from renewable sources, 10-hydroxystearic acid, 12-hydroxystearic acid, ricinoleic acid, and 16-hydroxyhexadecanoic acid, was carried out using commercially available immobilized lipases from Candida antarctica B, Thermomyces lanuginosus, and Pseudomonas stutzeri, as well as a native lipase. MALDI-TOF-MS and 2D-NMR analysis confirmed the formation of linear/branched and cyclic oligomers with average molecular weight around 1200 and polymerization degree up to 15. The appropriate selection of the biocatalyst and reaction temperature allowed the tailoring of the non-cyclic/cyclic copolymer ratio and increase of the total copolymer content in the reaction product above 80%. The catalytic efficiency of the best performing biocatalyst (Lipozyme TL) is evaluated during four reaction cycles, showing excellent operational stability. The thermal stability of the reaction products is assessed based on TG and DSC analysis. This new synthetic route for biobased oligomers with novel functionalities and properties could have promising biomedical applications.