A study of residual strains in aluminium-based dissimilar friction stir welds (FSWs) was performed by a novel approach that will be referred to as the Eigenstrain Reconstruction Method (ERM). The method is based on the theory of permanent inelastic strain (eigenstrain) as the basis for reconstructing full-field residual stress and strain states. The strain distributions evaluated by the angle-dispersive synchrotron X-ray diffraction were used to obtain the eigenstrain distributions by ERM. In order to build the FE eigenstrain model that forms the essential part of ERM implementation, the analysis of microstructure and diffraction peak profile (i.e., intensity and FWHM) was performed to understand the material mixing that occurred in the weld zone. The ERM approach allowed the approximate determination of the complete stress and strain state everywhere in the component. The resulting description is continuous, complete and consistent, in terms of satisfying the equilibrium, compatibility and boundary conditions. This is a significant improvement over the experimentally obtained raw data that only provides a limited knowledge of stress components at a number of selected measurement points, and over simple interpolation between these data points. It is concluded that ERM is a powerful tool for the analysis and use of full-field residual stress and strain distributions in engineering components and structures.