Using sustainable cement-based alternatives, such as secondary cementitious raw materials (SCMs), could be a viable option to decrease CO2 emissions resulting from cement production. Previously conducted studies to determine the optimal mix designs of concrete primarily focused on either experimental approaches or empirical modeling techniques. However, in these experimental approaches, few tests could be performed for optimization due to time restrictions and lack of resources, and empirical modeling methods cannot be relied on without external validation. The machine learning-based approaches are further characterized by certain shortcomings, including a smaller number of data points, a less robust connection among the controlling factors, and a lack of comparative analyses among machine learning models. Furthermore, the literature on predicting the performance of concrete utilizing binary SCMs (silica fume (SF) and ground granulated blast furnace slag (GGBS)) is not available. Therefore, to address these drawbacks, this research aimed to integrate ML-based models with experimental validations for accurate predictions of the compressive strength (CS) and tensile strength (TS) of concrete that includes SF and GGBS as SCMs. Three soft computing techniques, namely the ANN, ANFIS, and GEP methods, were used for prediction purposes. Eight major input parameters, including the W/B ratio, cement, GGBS, SF, coarse aggregates, fine aggregates, superplasticizer, and the age of the specimens, were considered for modeling. The validity of the established models was assessed by using external experimental validation criteria, statistical metrics, and performance measures. In addition, sensitivity and parametric analyses were performed. Based on statistical measures, the ANFIS models outperformed other models with higher correlation and lower statistical error values. However, the GEP models exhibited superior performance compared to ANFIS and ANN with respect to the closeness of the RMSE, MAE, RSE, and R2 values between the training, validation, and testing sets for both the CS and TS models. Experimental validation showed strong evidence for the applicability of the proposed models with an R2 of 0.88 and error percentages of less than 10%. Sensitivity and parametric investigations demonstrated that the input variables exhibited the patterns described in the experimental dataset and the available literature. Hence, the proposed models are accurate, have better prediction performance, and can be used for design purposes.