Engineered geopolymer composites (EGC) have emerged as a more environmentally friendly alternative to conventional engineered cementitious composites (ECC). These composites offer high mechanical and durability features. However, there is a lack of research on EGC, particularly with basic oxygen furnace (BOF) slag as a precursor and iron ore tailings (IOT) as a partial replacement to fine aggregate. Despite their effectiveness as industrial waste products in conventional concrete, this study aimed to determine the optimal compositions of fly ash (FA), steel fibres (SF), and IOT by varying their percentages. Overall, 150 mix combinations were tested, including six binder combinations, five combinations of fine aggregates, and five percentage variations in SF. Finally, one optimum mix was selected for each binder combination, based on the ultimate compressive strength values corresponding to the six optimal mixes. The compressive strengths of all the mixes were evaluated at both 7 and 28 days of curing, involving three replicate samples after oven curing (initial 24 h) followed by subsequent ambient curing until their respective ages. The highest observed compressive strength after 28 days was 41.77 MPa for 50 mm cubes. This strength was achieved with a composition of 60% FA, 1.5% SF, and 45% IOT. An increase in IOT percentage led to a nearly linear increase in strength, while the strength peaked at 1.5% for steel fibres. The addition of BOF slag significantly enhanced the compressive strength compared to mixes with full FA. A 40% fly ash replacement with BOF slag resulted in an average strength that was 39% higher than the combination with 100% fly ash. However, the strength growth decreased after a 10% replacement. Analysis of variance was conducted using the design of experiments methodology to determine the significance of the parameters and their interactions. All three independent parameters were found to be statistically significant, while their interactions were not. Utilizing Taguchi’s analysis method with the L25 orthogonal array, it was concluded that IOT percentage was the most influential parameter.