Graphene is an excellent material for long-distance spin transport but allows little spin manipulation. Transition-metal dichalcogenides imprint their strong spin–orbit coupling into graphene via the proximity effect, and it has been predicted that efficient spin-to-charge conversion due to spin Hall and Rashba–Edelstein effects could be achieved. Here, by combining Hall probes with ferromagnetic electrodes, we unambiguously demonstrate experimentally the spin Hall effect in graphene induced by MoS₂ proximity and for varying temperatures up to room temperature. The fact that spin transport and the spin Hall effect occur in different parts of the same material gives rise to a hitherto unreported efficiency for the spin-to-charge voltage output. Additionally, for a single graphene/MoS₂ heterostructure-based device, we evidence a superimposed spin-to-charge current conversion that can be indistinguishably associated with either the proximity-induced Rashba–Edelstein effect in graphene or the spin Hall effect in MoS₂. By a comparison of our results to theoretical calculations, the latter scenario is found to be the most plausible one. Our findings pave the way toward the combination of spin information transport and spin-to-charge conversion in two-dimensional materials, opening exciting opportunities in a variety of future spintronic applications.