We image the remnant magnetization configurations of CoFeB and permalloy nanotubes (NTs) using x-ray magnetic circular dichroism photoemission electron microscopy. The images provide direct evidence for flux-closure configurations, including a global vortex state, in which magnetization points circumferentially around the NT axis. Furthermore, micromagnetic simulations predict and measurements confirm that vortex states can be programmed as the equilibrium remnant magnetization configurations by reducing the ratio of the NT’s length and diameter.