Two-dimensional moiré materials provide a highly controllable solid-state platform for studies of quantum phenomena1–3. To date, experimental studies have focused on correlated electronic states, whereas correlated bosonic states in moiré materials have received less attention. Here we report the observation of a correlated dipolar excitonic insulator—a charge-insulating state driven by exciton formation4—in a device where a WSe2 monolayer and WSe2/WS2 moiré bilayer are coupled via Coulomb interactions. The system is a Mott insulator when all the holes reside in the moiré layer. Under an out-of-plane electric field, the holes can be continuously transferred to the WSe2 monolayer, but remain strongly bound to the empty moiré sites, effectively forming an interlayer exciton fluid in the moiré lattice. We further observe the emergence of local magnetic moments in the WSe2 monolayer induced by the strong interlayer Coulomb correlation. Our result provides a platform for realizing correlated quantum phenomena described by bosonic lattice models in a solid-state system, complementary to cold-atom setups5. © 2022, The Author(s), under exclusive licence to Springer Nature Limited.