Recently, friction stir welding method has been utilized to join aluminum to copper due to its significant features. Few investigations have been performed in dissimilar friction stir welded butt-joint of copper–aluminum so far and many features of the FSW procedure have been still unexplored and more studies are required. In this study, the effects of welding speed, rotational speed, and tool offset on the strength and microstructure of FSW joint of Al5083 and commercially pure copper plates was investigated. At low rotation speed (600 rpm), welding surface was coarse and weld flashes were thin with sharp edges; however thick flashes without sharp edge and rough surface were observed in very high rotation speed. The SEM fractography of fracture surfaces showed both dimples and cleavage planes. X-ray diffraction analysis results revealed several Al–Cu intermetallic compounds in stir zone which were Al4Cu9 and Al2Cu. Increasing the rotation speed from 800 to 1250 rpm for high value of offset (2 mm) showed significant decrease in tensile strength (p < 0.05). Increasing the offset value from 1 to 2 mm significantly decreased (p < 0.05) the tensile strength of joint for the specimen with 1250 rpm. The specimens with medium rotation speeds (800 rpm) revealed the best finish surface with the highest tensile strength.