A biodegradable antithrombotic conjugate having heparin and other anti-thrombotic moieties are introduced as side chains to the polymer backbone modified by click chemistry. Various bioabsorbable monomers and dimers such as valerolactone may be used in the monomer derivation, homo- and co-polymerization, and the conjugation with a biologically active molecule by click chemistry. A coating comprising a biocompatible and bioabsorbable polymer anti-thrombotic conjugate is applied to at least a portion of an implantable device to prevent or reduce the formation of thrombosis on the surface of the implantable device. A first or sub-layer of the coating is prepared by mixing a polymeric material and a biologically active agent with a solvent, thereby forming a homogeneous solution. A second or outer layer comprising the present anti-thrombotic conjugate may be applied over the inner drug-containing layers using, for example, a dip coating or spray coating process.