The main difficulty when joining magnesium (Mg) and aluminum (Al) alloys by fusion welding process lies in the existence of oxide films and formation of brittle intermetallic in the weld region. However, solid-state welding processes such as friction welding and diffusion bonding are suitable processes to join these two materials. The diffusion bonding process parameters such as bonding temperature, bonding pressure, holding time, and surface roughness of the bond specimen play a major role to determine the joint strength. In this investigation, an attempt was made to develop empirical relationships to predict the lap shear strength and bonding strength of diffusion bonded dissimilar joints of AZ61A magnesium and AA6061 aluminum alloys, incorporating the above-mentioned parameters. Response surface methodology (RSM) was applied to optimize the diffusion bonding process parameters to attain the maximum shear strength and bonding strength of the joint. From this investigation, it is found that the bonds fabricated with the bonding temperature of 420.43°C, bonding pressure of 7.70 MPa, holding time of 27.15 min, and surface roughness of 0.10 µm exhibited maximum shear strength and bonding strength of 51.24 and 72.10 MPa, respectively.