Experimentally measuring the diffusivities of CO₂ and H₂S in aqueous alkanolamine solutions presents an extremely challenging task. To overcome this challenge, we performed Molecular Dynamics (MD) simulations to study the effects of temperature and N-methyldiethanolamine (MDEA) concentration on self-diffusivities of CO₂ (D_CO2) and H₂S (D_H2S) in aqueous MDEA solutions. We compute the densities and viscosities of aqueous MDEA solutions for an MDEA concentration range of 10–50 wt% and a temperature range of 288–333 K showing an excellent agreement with experimental data from literature. We compute the self-diffusivity of MDEA (D_MDEA) in aqueous MDEA solutions and our findings show that the computed values of D_MDEA are in excellent agreement with experimental and simulation results from literature. The self-diffusivities D_CO2 and D_H2S in aqueous MDEA solutions are computed for a wide range of temperatures and MDEA concentrations and our results show that both D_CO2 and D_H2S depend significantly on temperature and MDEA concentration. We also show that both CO₂ and H₂S diffuse slower in aqueous MDEA solutions than in aqueous MEA solutions. By comparing the radial distribution functions of CO₂, H₂S, water, and MDEA, we show that H₂S has stronger interactions with the surrounding molecules than CO₂, which makes H₂S diffuse slower in aqueous MDEA solutions. We also investigate the densities and viscosities of acid gas loaded aqueous MDEA solutions and self-diffusivities of the reaction products of CO₂ and H₂S with aqueous MDEA solutions. We show that the self-diffusivities of CO₂-loaded solutions significantly decrease with increasing CO₂ loading while the self-diffusivities of H₂S-loaded solutions do not change with changing H₂S loading. Our results will be helpful in the design and optimization of acid gas removal units.