Transition metal dichalcogenides are optically active, layered materials promising for fast optoelectronics and on-chip photonics. We demonstrate electrically driven single-photon emission from localized sites in tungsten diselenide and tungsten disulphide. To achieve this, we fabricate a light-emitting diode structure comprising single-layer graphene, thin hexagonal boron nitride and transition metal dichalcogenide mono- and bi-layers. Photon correlation measurements are used to confirm the single-photon nature of the spectrally sharp emission. These results present the transition metal dichalcogenide family as a platform for hybrid, broadband, atomically precise quantum photonics devices.