This paper presents the theoretical screening of 23 low-cost deep eutectic solvents (DESs) as absorbents for effective removal of the main impurities from biogas streams using a conductor-like screening model for real solvents (COSMO-RS). Based on thermodynamic parameters, i.e., the activity coefficient, excess enthalpy, and Henry’s constant, two DESs composed of choline chloride: urea in a 1:2 molar ratio (ChCl:U 1:2), and choline chloride: oxalic acid in a 1:2 molar ratio (ChCl:OA 1:2) were selected as the most effective absorbents. The σ-profile and σ-potential were used in order to explain the mechanism of the absorptive removal of CO2, H2S, and siloxanes from a biogas stream. In addition, an economic analysis was prepared to demonstrate the competitiveness of new DESs in the sorbents market. The unit cost of 1 m3 of pure bio-methane was estimated to be in the range of 0.35–0.37 EUR, which is comparable to currently used technologies.