In this study, the adsorption of CO2 and H2S has been investigated on commercial activated carbon Desorex K43 impregnated with K2CO3, NaOH, or Fe2O3 in order to assess their potential for “upgrading” and desulfurization of biogas or contaminated natural gas. Different chemical Fourier transformed infrared spectra (FTIR), X-ray fluorescence (XRF) and pH measurements and textural characterization techniques (N2 adsorption/desorption isotherms) were used to study the material surface and confirm the presence of K, Na, and Fe. Gravimetric experiments of single and binary gas sorption isotherms were used to evaluate CO2 uptake and selectivity with respect to CH4. Breakthrough curves under dry and humid conditions were performed to assess the adsorption of H2S. The materials studied showed high adsorption capacities for both gases: in the range from 0.85 to 4.58 mmol g–1 for H2S and from 1.61 to 1.88 mmol g–1 CO2, under dry conditions and 1 bar. Furthermore, the selectivity of the activated carbons for CO2 in relation to CH4 was in the range of 1.2–2.4, Desorex K43-BG being the material with higher adsorption capacity for gases under study. The data obtained by the adsorption experiments were correlated with the textural characteristics and the chemical properties of the materials, which allowed one to identify how promising an adsorbent is for the removal of acidic gases from biogas to obtain biomethane. The best compromise between H2S adsorption and CO2/CH4 selectivity was found for the sample containing Na (Desorex K43-Na), which benefited from both a basic surface chemistry and pore size distribution restricted to the micropore range.