Two-dimensional electronic-vibrational spectroscopy (2DEVS) is a useful technique for studying the structure and dynamics of photoexcited molecules via monitoring of the vibrational spectrum in real-time. However, quantitative modeling or prediction of experimental spectra has been hampered by the lack of a firm theoretical basis for this quantity. Here, we develop a useful theory of 2DEVS and show that the time-dependent line shape of the 2DEVS spectrum provides invaluable information on the cross-correlation function of the solvation dynamics and vibrational spectral diffusion. The center and nodal line slopes of each 2DEVS peak are determined by the associated cross-electronic- vibrational frequency-frequency correlation function, which is shown to be related to the intermolecular interactions and vibrational anharmonicities. The present theory of 2DEVS would thus be of use for a refined understanding of the 2DEVS spectra of reactive chemical and biological systems. We anticipate that further development of the expressions developed here will illuminate the application of 2DEVS studies of vibronically induced energy and electron transfer in functional materials.