Electronic absorption spectra and the frontier orbitals of 1-arylazo-2-naphtol dyes are computed and analyzed in four models, namely in the gas phase (model I), in a solvent (model I+CPCM), adsorbed on the cellulose surface (model II), and model II in the presence of solvent (model II+CPCM) via time-dependent density functional theory (TD-DFT) and conductor-like polarizable continuum model (CPCM) at the B3LYP/6-31G** level of theory. A bathochromic shift is observed for the lmax peak due to both short-range and long-range interactions of the non-ionic dyes with cellulose, while the ionic dyes exhibit hypsochromic shift in their lmax peak. The results predict that the studied dyes should be nearly yellow after being adsorbed on cellulose with excellent color strength. Furthermore, the ionic dyes are suitable for the dyeing of cellulose fibers. The nuclear magnetic resonance (NMR) chemical shieldings calculated for the azo dyes in the gas phase and adsorbed states and for their tautomeric equilibrium mixtures show that the NMR technique can be used successfully to follow the dyeing process.