This research investigates the heat treatment parameters of 6061-aluminum alloy to enhance its mechanical properties. The Taguchi design-of-experiments (DOE) method was employed to systematically examine the effects of solutionizing temperature, solutionizing time, aging temperature, and aging time on the tensile strength of the alloy. Mechanical testing suggested a major influence of solutionizing and aging temperatures on the ultimate tensile strength of the alloy. The samples subjected to a solutionizing temperature of 540 °C for 3 h, followed by aging at 170 °C for 18 h, exhibited the highest ultimate tensile strength (293.7 MPa). Conversely, the samples processed at the lowest levels of these parameters displayed the lowest ultimate tensile strength (193.7 MPa). Microstructural analysis confirmed the formation of equiaxed grains, strengthening precipitates, precipitate clusters, and β (Mg2Si) precipitates alongside Fe-Al-Si dispersoids. Energy-dispersive X-ray spectroscopy (EDS) analysis detected the presence of elemental precursors of β phase (Al-Mg-Si) and dispersoid-forming elements (Al-Fe-Si). X-ray diffraction spectroscopy (XRD) analysis revealed the persistence of the β phase in the alloy, indicating its contribution to the improved mechanical properties, which are mainly obtained by aging precipitation phases. Fracture analysis showed a ductile fracture mechanism, and examining fractured samples supported the findings of enhanced tensile properties resulting from the adequate selection of heat treatment parameters. We employed ANOVA (analysis of variance) to analyze the DOE results, using a multiple regression model to express the ultimate tensile strength of the alloy in terms of the variables used in the design. This yielded an adjusted coefficient of determination of 89.75%, indicating a high level of explained variability in the test data for evaluating the model’s predictive capacity.