Ensembles of indirect or interlayer excitons (IXs) are intriguing systems to explore classical and quantum phases of interacting bosonic ensembles. IXs are composite bosons that feature enlarged lifetimes due to the reduced overlap of the electron-hole wave functions. We demonstrate electric Field control of indirect excitons in MoS2/WS2 hetero-bilayers embedded in a field effect structure with few-layer hexagonal boron nitrite as insulator and few-layer graphene as gate-electrodes. The different strength of the excitonic dipoles and a distinct temperature dependence identify the indirect excitons to stem from optical interband transitions with electrons and holes located in different valleys of the hetero-bilayer featuring highly hybridized electronic states. For the energetically lowest emission lines, we observe a field-dependent level anticrossing at low temperatures. We discuss this behavior in terms of coupling of electronic states from the two semiconducting monolayers resulting in spatially delocalized excitons of the hetero-bilayer behaving like an artificial van der Waals solid. Our results demonstrate the design of novel nano-quantum materials prepared from artificial van der Waals solids with the possibility to in-situ control their physical properties via external stimuli such as electric fields.