Experimental equilibrium solubility data are reported for hydrogen sulfide in mixtures of tetramethylene sulfone (sulfolane) with 15, 30 and 50 wt.% diethanolamine, and for carbon dioxide in a mixture of sulfolane with 50 wt.% diethanolamine in the temperature range 303.15-373.15 K from 15 up to 2296 kPa of solute partial pressure. The results of the gas solubility measurements are presented as a partial pressure of the solute against its mole fraction in the solvent mixture, and also against its mole ratio with respect to diethanolamine. For a given temperature, the solubility of either solute increases as the pressure increases. The solubility of the hydrogen sulfide increases as the concentration of diethanolamine increases. Exothermic values of the enthalpy of solution for hydrogen sulfide and carbon dioxide were obtained from solubility data.