The monolayer transition metal dichalcogenides have recently attracted much attention owing to their potential in valleytronics, flexible and low-power electronics, and optoelectronic devices. Recent reports have demonstrated the growth of large-size two-dimensional MoS₂ layers by the sulfurization of molybdenum oxides. However, the growth of a transition metal selenide monolayer has still been a challenge. Here we report that the introduction of hydrogen in the reaction chamber helps to activate the selenization of WO₃, where large-size WSe₂ monolayer flakes or thin films can be successfully grown. The top-gated field-effect transistors based on WSe₂ monolayers using ionic gels as the dielectrics exhibit ambipolar characteristics, where the hole and electron mobility values are up to 90 and 7 cm²/Vs, respectively. These films can be transferred onto arbitrary substrates, which may inspire research efforts to explore their properties and applications. The resistor-loaded inverter based on a WSe₂ film, with a gain of ∼13, further demonstrates its applicability for logic-circuit integrations.