Azo-hydrazone tautomerism in azo dyes has been modeled by using density functional theory (DFT) at the B3LYP/6-31+G(d,p) level of theory. The most stable tautomer was determined both for model compounds and for azo dyes Acid Orange 7 and Solvent Yellow 14. The effects of the sulfonate group substitution and the replacement of the phenyl group with naphthyl on the tautomer stability and on the behavior in solvent have been discussed. Intramolecular hydrogen bond energies have been estimated for the azo and hydrazone tautomers to derive a relationship between the tautomer stability and the hydrogen bond strength. The transition structures for proton transfer displayed resonance assisted strong hydrogen bonding properties within the framework of the electrostatic-covalent hydrogen bond model (ECHBM). Evolution of the intramolecular hydrogen bond with changing structural and environmental factors during the tautomeric conversion process has been studied extensively by means of the atoms-in-molecules (AIM) analysis of the electron density. The bulk solvent effect was examined using the self-consistent reaction field model. Special solute-solvent interactions were further investigated by means of quantum mechanical calculations after defining the first-solvation shell by molecular dynamics simulations. The effect of cooperative hydrogen bonding with solvent molecules on the tautomer stability has been discussed.