A microscopic statistical mechanical theory of solvation dynamics is presented. The theory is capable of reproducing the characteristic multiphasic behavior of the solvation correlation function typically observed in the time-resolved spectroscopic studies. The fast initial decay of the solvation correlation function is modeled on the basis of a short-time expansion, while the slowly varying long-time tail is computed within the mode-coupling theory formalism. Comparison with simulation for nonpolar solvation shows that the present theory provides a very substantial improvement over the commonly used time-dependent density functional and surrogate Hamiltonian treatments of the slow component of solvation dynamics. In addition, the range of applicability of the results obtained in this study is much wider compared to the other theories. The mode-coupling theory of solvation is tested for model nonpolar systems consisting of both a neat fluid and a system, where the chromophore size is significantly different from that of the solvent particles. A systematic study of the dependence of the solvation time scales on the size of the chromophore is carried out.