A method is described for incorporating the vibronic transitions of a solute molecule in the calculation of the time evolution of its fluorescence spectrum in a polar solvent. In this initial article, systems are treated in which the intramolecular vibrational relaxation is much faster than the observed delay time. The overall fluorescence spectrum is then shown to be a convolution of the steady-state absorption and emission spectra of the solute in a nonpolar solvent and the time-dependent emission line shape arising only from polar interactions. Calculations are made for coumarin 153 in acetonitrile, using the dielectric dispersion data of the solvent available from experimental measurements. The results are in encouraging agreement with experimental spectra. Results are also given for the dynamic Stokes shift in methanol.