Solid-state welding processes, particularly friction-stir welding (FSW), offer significant advantages for joining different aluminum alloys due to their good mechanical performance, energy efficiency, and cost-effectiveness. The FSW of the AA5052-H32 and AA6261-T6 alloys has not been previously reported. In this study, the effects of the main FSW process parameters on the mechanical behavior of different AA5052/AA6261 alloy joints were systematically investigated. A full factorial experimental design was applied, considering the tool rotation speed (900–1800 rpm) and the welding speed (56–252 mm/min) as control factors, along with their ratio (Rs/Ws). The results of the tensile tests reveal that the joint strength is strongly affected by the interaction between the rotation and welding speeds, with the Rs/Ws ratio is identified as a key parameter governing material flow, plastic deformation, and defect formation. The maximum tensile strength, approximately 198 MPa, corresponding to a mechanical efficiency of 84.4%, was achieved at 1800 rpm and 7 rev/mm, a condition that favored effective material mixing and a defect-free interfacial bond (≈162–186 MPa). The microhardness profiles showed a minimum of approximately 40–50 HV within the TMAZ, on the advancing side. In general, clear quantitative relationships were established between the process parameters and the mechanical properties, which allowed for the identification of optimal operating conditions to produce high-quality FSW joints between the dissimilar materials AA5052/AA6261.