  Stacking monolayers of transition metal dichalcogenides into a
heterostructure with a finite twist-angle gives rise to artificial moir\'e
superlattices with a tunable periodicity. As a consequence, excitons experience
a periodic potential, which can be exploited to tailor optoelectronic
properties of these materials. While recent experimental studies have confirmed
twist-angle dependent optical spectra, the microscopic origin of moir\'e
exciton resonances has not been fully clarified yet. Here, we combine first
principle calculations with the excitonic density matrix formalism to study
transitions between different moir\'e exciton phases and their impact on
optical properties of the twisted MoSe$_2$/WSe$_2$ heterostructure. At angles
smaller than 2$^{\circ}$ we find flat, moir\'e trapped states for inter- and
intralayer excitons. This moir\'e exciton phase drastically changes into
completely delocalized states already at 3$^{\circ}$. We predict a linear and
quadratic twist-angle dependence of excitonic resonances for the
moir\'e-trapped and delocalized exciton phase, respectively. Our work provides
microscopic insights opening the possibility to tailor moir\'e exciton phases
in van der Waals superlattices.
