A microscopic statistical mechanical theory of electronic solvatochromism in supercritical fluids is presented. A microscopic expression for the solvent-induced electronic line shift is given, which involves the solute-solvent radial distribution function and interaction potentials. The radial distribution function is obtained from the integral equation theory of inhomogeneous fluids. The theory is applied to study the experimentally observed nonlinear density dependence of spectral line shifts in supercritical fluids in the near critical region. Model calculations of spectral shifts are performed for a range of solvent densities and temperatures and model potential parameters. In addition, a quantitative comparison of the theory with experimental data on electronic line shifts is performed, and the agreement is satisfactory.