The growing commercial availability of carbon nanotube (CNT) macro-assemblies such as sheet and yarn is making their use in structural composite components increasingly feasible. However, the mechanical properties of these materials continue to trail those of state-of-the-art carbon fiber composites due to relatively weak inter-tube load transfer. Forming covalent links between adjacent CNTs promises to mitigate this problem, but it has proven difficult in practice to introduce them chemically within densified and aligned CNT materials due to their low permeability. To avoid this limitation, this work explores the combination of pulsed electrical current, temperature, and pressure to introduce inter-CNT bonds. Reactive molecular dynamics simulations identify the most probable locations, configurations, and conditions for inter-nanotube bonds to form. This process is shown to introduce covalent linkages within the CNT material that manifest as improved macroscale mechanical properties. The magnitude of this effect increases with increasing levels of prealignment of the CNT material, promising a new synthesis pathway to ultralight structural materials with specific strengths and stiffnesses exceeding 1 and 100 GPa/(g/cu.cm), respectively.