Deep eutectic solvents (DESs) are novel environment-friendly media for a variety of applications. In order to obtain insight into the structure and dynamics of some less-explored DESs comprising ethylene glycol and tetraalkylammonium bromide salts with variable alkyl chain length, we have captured complete dynamics occurring in these solvents in a timescale of few femtoseconds to several nanoseconds by monitoring the time-dependent fluorescence Stokes shift of coumarin 153 employing a combination of time-correlated single-photon counting and fluorescence upconversion techniques. The solvent response function constructed from the measured data reveals a subpicosecond component (similar to 0.8 ps, 20-35%) in addition to a slow component (180-475 ps) with a distribution of relaxation time. The slow time component is found to be strongly dependent on the viscosity of the medium, indicating that it arises from the diffusive motions of the solvent constituents into and out of the solvation shell, whereas the ultrafast time component, which is nearly independent of the solvent viscosity, arises from fast local motions of the constituents in the immediate vicinity of the solute molecule.