Bioprosthetic devices include an exterior biological tissue member which at least partly defines a cavity, and a proteinaceous biopolymer which fills the cavity, and intercalates and is chemically bound (fixed) to the tissue of the surrounding biological tissue member. In preferred forms, the bioprosthetic device is a bioprosthetic vertebral disc having a fibrillar outer annulus which surrounds and defines an interior cavity and is formed by removal of at least a substantial portion of the natural gelatinous core therefrom. The cavity defined by the fibrillar outer annulus may then be filled with a flowable proteinaceous biopolymer. Preferably, the proteinaceous biopolymer is a liquid mixture comprised of human or animal-derived protein material and a di- or polyaldehyde, which are allowed to react in situ to form a cross-linked biopolymer within the cavity. The liquid mixture may be formed in advance of being introduced into the cavity, or may be formed simultaneously during introduction into the cavity.