The adsorption of two different organic molecules cyanidin glucoside (C21O11H20) and TA-St-CA on anatase (101) and (001) nanowires has been investigated using the standard and the range separated hybrid density functional theory calculations. The electronic structures and optical spectra of resulting dye-nanowire combined systems show distinct features for these types of photochromophores. The lowest unoccupied molecular orbital of the natural dye cyanidin glucoside is located below the conduction band of the semiconductor while, in the case of TA-St-CA, it resonates with the states inside the conduction band. The wide-bandgap anatase nanowires can be functionalized for solar cells through electron-hole generation and subsequent charge injection by these dye sensitizers. The intermolecular charge transfer character of Donor-π-Acceptor type dye TA-St-CA is substantially modified by its adsorption on TiO2 surfaces. Cyanidin glucoside exhibits relatively stronger anchoring on the nanowires through its hydroxyl groups. The atomic structures of dye-nanowire systems re-optimized with the inclusion of nonlinear solvation effects showed that the binding strengths of both dyes remain moderate even in ionic solutions.