The large-scale growth of semiconducting thin films forms the basis of modern electronics and optoelectronics. A decrease in film thickness to the ultimate limit of the atomic, sub-nanometre length scale, a difficult limit for traditional semiconductors (such as Si and GaAs), would bring wide benefits for applications in ultrathin and flexible electronics, photovoltaics and display technology. For this, transition-metal dichalcogenides (TMDs), which can form stable three-atom-thick monolayers, provide ideal semiconducting materials with high electrical carrier mobility, and their large-scale growth on insulating substrates would enable the batch fabrication of atomically thin high-performance transistors and photodetectors on a technologically relevant scale without film transfer. In addition, their unique electronic band structures provide novel ways of enhancing the functionalities of such devices, including the large excitonic effect, bandgap modulation, indirect-to-direct bandgap transition, piezoelectricity and valleytronics. However, the large-scale growth of monolayer TMD films with spatial homogeneity and high electrical performance remains an unsolved challenge. Here we report the preparation of high-mobility 4-inch wafer-scale films of monolayer molybdenum disulphide (MoS2) and tungsten disulphide, grown directly on insulating SiO2 substrates, with excellent spatial homogeneity over the entire films. They are grown with a newly developed, metal-organic chemical vapour deposition technique, and show high electrical performance, including an electron mobility of 30 cm(2) V(-1) s(-1) at room temperature and 114 cm(2) V(-1) s(-1) at 90 K for MoS2, with little dependence on position or channel length. With the use of these films we successfully demonstrate the wafer-scale batch fabrication of high-performance monolayer MoS2 field-effect transistors with a 99% device yield and the multi-level fabrication of vertically stacked transistor devices for three-dimensional circuitry. Our work is a step towards the realization of atomically thin integrated circuitry.