The present investigation aims to establish the influence of tool axis offset and the relative position of materials on the stir zone (SZ) material flow and joint characteristics of friction stir (FS) butt welded dissimilar AA5083-H111 and AA7050-T7651 aluminium alloys. The FS welding trials were conducted by systematically varying the tool axis offset from zero to 1 mm, with an increment of 0.25 mm, to both the advancing side (AS) and retreating side (RS) of the joint by keeping AA7050 and AA5083 alloys at the AS and RS of the joint, respectively. The welding speed, tool rotational speed, axial force and tool tilt angle were held constant. The results showed that for the given relative position of the alloys, the tool axis offset has significant influence on the SZ material flow pattern and the evolution of microstructure in the joint zone. The microhardness has a heterogeneous distribution across the joint and it is found to be sensitive to the tool axis offset. The highest hardness values are observed for the joints FS welded at 1 mm tool axis offset to the AS and the lowest for the joints welded at 1 mm tool axis offset to the RS of the joint. The joint fabricated at 0.5 mm tool axis offset to the AS has exhibited the highest joint strength of 303 MPa (joint efficiency of 98.4 %). Also, within the limits of tool axis offset experimented, the joint integrity is less sensitive to the variation of tool axis offset to both the AS and RS of the joint. The softening of the HAZ on the weaker AA5083 alloy side (for high heat generation cases) and the weakening of the SZ towards the bottom (for low heat generation cases) are the main factors limiting the joint strength. The studies showed that in FSW of dissimilar 5xxx and 7xxx alloys, appropriate selection of tool axis offset and relative position of the alloys are critical for producing joints with excellent joint efficiency.