Combining surface-initiated, TdT (terminal deoxynucleotidyl transferase) catalyzed enzymatic polymerization (SI-TcEP) with precisely engineered DNA origami nanostructures (DONs) presents an innovative pathway for the generation of stable, polynucleotide brush-functionalized DNA nanostructures. We demonstrate that SI-TcEP can site-specifically pattern DONs with brushes containing both natural and non-natural nucleotides. The brush functionalization can be precisely controlled in terms of the location of initiation sites on the origami core and the brush height and composition. Coarse-grained simulations predict the conformation of the brush-functionalized DONs that agree well with the experimentally observed morphologies. We find that polynucleotide brush-functionalization increases the nuclease resistance of DONs significantly, and that this stability can be spatially programmed through the site-specific growth of polynucleotide brushes. The ability to site-specifically decorate DONs with brushes of natural and non-natural nucleotides provides access to a large range of functionalized DON architectures that would allow for further supramolecular assembly, and for potential applications in smart nanoscale delivery systems.