The understanding of cell material interactions is important for creating personalized implants for tissue engineering. This has resulted in an interest in developing polymers with functional groups with the possibility of controlling the macromolecular surface. We have in a one-pot reaction synthesized a series of amorphous and degradable polyester-based copolymers with active functional groups by copolymerization of 2-methylene-1,3-dioxepane and glycidyl methacrylate. The properties of the final polymers were varied by varying the feed ratios of the monomers, and it was seen that it was possible to control the amount of active functional groups. The resulting epoxy-functionalized polyester was further modified by covalent immobilization of heparin. The heparinization was done in order, in a future aspect, to enhance the osteogenic differentiation of mesenchyrnal stem cells. Heparin binds directly with the growth factor bone morphogenetic protein-2 and helps to retain its activity. The molecular structure of the copolymers was characterized by nuclear magnetic resonance, size exclusion chromatography, and Fourier transform infrared spectroscopy. Differential scanning calorimetry and tensile testing showed that the monomer feed ratio had a great influence on the properties of the final polymer and that it thus was possible to control the mechanical properties to suit an intended application. The presence of heparin was verified by toluidine blue staining, and all of the films tested showed positive signals for heparin.