The transient absorption spectroscopy of photoexcited equilibrium hydrated electrons is computed from quantum nonadiabatic molecular dynamics simulations. The results strongly parallel ultrafast spectral transients measured in recent experiments (Barbara and co-workers, J. Chem. Phys. 1993, 98, 5996 and J. Phys. Chem., in press), with spectral dynamics that cannot be adequately described by a simple two-state kinetic model. Computed transient spectra with various absorption and bleaching contributions removed are used to explore the microscopic physics underlying the complex behavior. The observed dispersion in excited-state lifetimes and rapid reequilibration of the electron after the radiationless transition to the ground state lead to the conclusion that spectral changes due to solvent cooling after this transition are of little importance to the transient spectroscopy. Instead, the observed complexity of the ultrafast spectral dynamics is shown to be the result of a combination of spectral changes due to excited-state solvation and ground-state bleaching dynamics.