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Determining the solubility of non-hydrocarbon gases such as carbon dioxide (CO2) and nitrogen (N2) in water and brine is one of the most controversial challenges in the oil and chemical industries. Although many researches have been conducted on solubility of gases in brine and water, very few researches investigated the solubility of power plant flue gases (CO2–N2 mixtures) in aqueous solutions. In this study, using six intelligent models, including Random Forest, Decision Tree (DT), Gradient Boosting-Decision Tree (GB-DT), Adaptive Boosting-Decision Tree (AdaBoost-DT), Adaptive Boosting-Support Vector Regression (AdaBoost-SVR), and Gradient Boosting-Support Vector Regression (GB-SVR), the solubility of CO2–N2 mixtures in water and brine solutions was predicted, and the results were compared with four equations of state (EOSs), including Peng–Robinson (PR), Soave–Redlich–Kwong (SRK), Valderrama–Patel–Teja (VPT), and Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). The results indicate that the Random Forest model with an average absolute percent relative error (AAPRE) value of 2.8% has the best predictions. The GB-SVR and DT models also have good precision with AAPRE values of 6.43% and 7.41%, respectively. For solubility of CO2 present in gaseous mixtures in aqueous systems, the PC-SAFT model, and for solubility of N2, the VPT EOS had the best results among the EOSs. Also, the sensitivity analysis of input parameters showed that increasing the mole percent of CO2 in gaseous phase, temperature, pressure, and decreasing the ionic strength increase the solubility of CO2–N2 mixture in water and brine solutions. Another significant issue is that increasing the salinity of brine also has a subtractive effect on the solubility of CO2–N2 mixture. Finally, the Leverage method proved that the actual data are of excellent quality and the Random Forest approach is quite reliable for determining the solubility of the CO2–N2 gas mixtures in aqueous systems.