A vertically aligned nanotube array of titanium oxide was fabricated on the surface of titanium substrate by anodization. The nanotubes were then treated with NaOH solution to make them bioactive, and to induce growth of hydroxyapatite (bone-like calcium phosphate) in a simulated body fluid. It is shown that the presence of TiO2 nanotubes induces the growth of a "nano-inspired nanostructure", i.e., extremely fine-scale (approximately 8 nm feature) nanofibers of bioactive sodium titanate structure on the top edge of the approximately 15 nm thick nanotube wall. During the subsequent in-vitro immersion in a simulated body fluid, the nano-scale sodium titanate, in turn, induced the nucleation and growth nano-dimensioned hydroxyapatite (HAp) phase. The kinetics of HAp formation is significantly accelerated by the presence of the nanostructures. Such TiO2 nanotube arrays and associated nanostructures can be useful as a well-adhered bioactive surface layer on Ti implant metals for orthopaedic and dental implants, as well as for photocatalysts and other sensor applications.