Combining ab initio density functional theory with the Dirac-Bloch and gap equations, excitonic properties of transition-metal dichalcogenide hetero-bilayers with type-II band alignment are computed. The existence of interlayer excitons is predicted, whose binding energies are as large as 350 meV, only roughly 100 meV less than those of the coexisting intralayer excitons. The oscillator strength of the interlayer excitons reaches a few percent of the intralayer exciton resonances and their radiative lifetime is two orders of magnitude larger than that of the intralayer excitons.