The use of graphene and other two-dimensional materials in next-generation electronics is hampered by the significant damage caused by conventional lithographic processing techniques employed in device fabrication. To reduce the density of defects and increase mobility, Joule heating is often used since it facilitates lattice reconstruction and promotes self-repair. Despite its importance, an atomistic understanding of the structural and electronic enhancements in graphene devices enabled by current annealing is still lacking. To provide a deeper understanding of these mechanisms, atomic recrystallization and electronic transport in graphene nanoribbon (GNR) devices are investigated using a combination of experimental and theoretical methods. GNR devices with widths below 10 nm are defined and electrically measured in situ within the sample chamber of an aberration-corrected transmission electron microscope. Immediately after patterning, we observe few-layer polycrystalline GNRs with irregular sp2-bonded edges. Continued structural recrystallization towards a sharp, faceted edge is promoted by increasing application of Joule heat. Monte Carlo-based annealing simulations reveal that this is a result of concentrated local currents at lattice defects, which in turn promotes restructuring of unfavorable edge structures towards an atomically sharp state. We establish that intrinsic conductance doubles to 2.7 e2/h during the recrystallization process following an almost threefold reduction in device width, which is attributed to improved device crystallinity. In addition to the observation of consistent edge bonding in patterned GNRs, we further motivate the use of bonded bilayer GNRs for future nanoelectronic components by demonstrating how electronic structure can be tailored by an appropriate modification of the relative twist angle of the bonded bilayer.