A general analytical expression for the transient fluorescence spectrum is derived. The formation of a wave packet in the excited state of a fluorophore is described, assuming that the pump pulse has a Gaussian timeprofile. The expression explicitly connects the relaxation characteristics of the medium with the spectral dynamics of a fluorophore. Fitting the expression to experimental spectral dynamics allows obtaining the solvent relaxation function. So far this approach was applicable for the analysis of experimental data when the pump pulse does not populate excited sublevels of intramolecular high-frequency vibrational modes. Here, the approach is generalized to include vibrational relaxation in the excited electronic state. In this case, fitting to the experimental spectral dynamics provides reliable information not only on the solvent relaxation, but also on the relaxation time constants of intramolecular high-frequency vibrational modes. This approach is applied to the excited state dynamics of coumarin 153 in multiple solvents, obtained from broadband fluorescence upconversion spectroscopy.