Experimental studies of solvation dynamics in imidazolium-based ionic liquids (ILs) have revealed complex kinetics over a broad range of time scales from femtoseconds to tens of nanoseconds. Microsecond-length molecular dynamics (MD) simulations of coumarin 153 (C153) in 1-ethyl-3-methyl imidazolium tetrafluoroborate, [emim][BF4], were performed to reveal the molecular-level mechanism for solvation dynamics in imidazolium-based ILs over the full range of time scales accessed in the experiments. The solvation response of C153 in [emim][BF4] compared favorably with experiment. An analysis of the structure of the IL in the vicinity of the C153 dye revealed preferential solvation by the [emim] cations. Despite this observation, decomposition of the solvation response into components from the anions and cations and also from translational and rotational motions shows that translations of the [BF4] anions are the dominant contributor to solvation dynamics. The kinetics for the translation of the [BF4] anions into and out of the first solvation shell of the dye were found to mimic the kinetic profile of the solvation dynamics response. This mechanism for solvation dynamics contrasts dramatically with conventional polar liquids in which solvent rotations are generally responsible for the response.