Self-compacting concrete (SCC) is a special form of high-performance concrete that is highly efficient in its filling, flowing, and passing abilities. In this study, an attempt has been made to model the compressive strength (CS) of SCC mixes using machine-learning approaches. The SCC mixes were designed considering lightweight expandable clay aggregate (LECA) as a partial replacement for coarse aggregate; ground granulated blast-furnace slag (GGBS) as a partial replacement for binding material (cement); and incinerated bio-medical waste ash (IBMWA) as a partial replacement for fine aggregate. LECA, GGBS, and IBMWA were replaced with coarse aggregate, cement, and fine aggregate, respectively at different substitution levels of 10%, 20%, and 30%. M30-grade SCC mixes were designed for two different water/binder ratios—0.40 and 0.45—and the CS of the SCC mixes was experimentally determined along with the fresh state properties assessed by slump-flow, L-box, J-ring, and V-funnel tests. The CS of the SCC mixes obtained from the experimental analysis was considered for machine learning (ML)-based modeling using paradigms such as artificial neural networks (ANN), gradient tree boosting (GTB), and CatBoost Regressor (CBR). The ML models were developed considering the compressive strength of SCC as the target parameter. The quantities of materials (in terms of %), water-to-binder ratio, and density of the SCC specimens were used as input variables to simulate the ML models. The results from the experimental analysis show that the optimum replacement percentages for cement, coarse, and fine aggregates were 30%, 10%, and 20%, respectively. The ML models were successful in modeling the compressive strength of SCC mixes with higher accuracy and the least errors. The CBR model performed relatively better than the other two ML models, with relatively higher efficiency (KGE = 0.9671) and the least error (mean absolute error = 0.52 MPa) during the testing phase.