Deep eutectic solvents (DESs) are emerging as an alternative media for the sequestration of greenhouse gases such as CO2 and SO2. Herein, we performed ab initio molecular dynamics (AIMD) simulations to elucidate the solvation structure around CO2 and SO2 in choline chloride-based DESs, namely, reline and ethaline. We show that in all four systems the structures of the nearest neighbor shells around these molecules are distinct. We observe that because of the electrophilic character, the carbon atom of CO2 and the sulfur atom of SO2 are preferentially solvated by the chloride anions. The strength of the correlation between the chloride anions and the sulfur atom is much stronger because of charge transfer, which is more profound in ethaline DES. In both DESs, the choline cations are found to be closer to the oxygen atoms of CO2 and SO2. We observe that upon changing the solute from CO2 to SO2 the nearest neighbor solvation structure changes drastically; while the chloride anions prefer to stay in a circular shell around the carbon atom of CO2 they are found to be much more localized near the sulfur atom of SO2. The solvation shells formed by the urea molecules in reline and EG molecules in ethaline also overlap with that of the chloride anion around CO2 In ethaline, the hydroxyl group of the choline cation is found to be closer to the solute molecules as compared to its ammonium headgroup.