In superlattices of twisted semiconductor monolayers, tunable moir\'e potentials emerge, trapping excitons into periodic arrays. In particular, spatially separated interlayer excitons are subject to a deep potential landscape and they exhibit a permanent dipole providing a unique opportunity to study interacting bosonic lattices. Recent experiments have demonstrated density-dependent transport properties of moir\'e excitons, which could play a key role for technological applications. However, the intriguing interplay between exciton-exciton interactions and moir\'e trapping has not been well understood yet. In this work, we develop a microscopic theory of interacting excitons in external potentials allowing us to tackle this highly challenging problem. We find that interactions between moir\'e excitons lead to a delocalization at intermediate densities and we show how this transition can be tuned via twist angle and temperature. The delocalization is accompanied by a modification of optical moir\'e resonances, which gradually merge into a single free exciton peak. The predicted density-tunability of the supercell hopping can be utilized to control the energy transport in moir\'e materials.