Biomimetic artificial prostheses which are made from polyester, such as polyethylene terephthalate, and a method for the biomimetic functionalization of such prostheses. The method includes a step involving the grafting of biologically-active polymers or copolymers to the polyester surface of the prostheses, the grafting step consisting of the peroxidation of the surface by ozonation followed by a step including the radical polymerization of a solution of at least one monomer. The method also includes an optional step consisting in impregnating the prostheses with type I and/or II collagen and/or fibronectins. The prostheses thus obtained enable a normal and uniform regrowth of the fibroblasts, thereby significantly improving the biological integration of such polyester prostheses.