High-quality and large-scale growth of monolayer molybdenum disulfide (MoS₂) has caught intensive attention because of its potential in many applications due to unique electronic properties. Here, we report the wafer-scale growth of high-quality monolayer MoS₂ on single-crystalline sapphire and also on SiO₂ substrates by a facile metal-organic chemical vapor deposition (MOCVD) method. Prior to growth, an aqueous solution of sodium molybdate (Na₂MoO₄) is spun onto the substrates as the molybdenum precursor and diethyl sulfide ((C₂H₅)₂S) is used as the sulfur precursor during the growth. The grown MoS₂ films exhibit crystallinity, good electrical performance (electron mobility of 22 cm²·V^-1·s^-1) and structural continuity maintained over the entire wafer. The sapphire substrates are reusable for subsequent growth. The same method is applied for the synthesis of tungsten disulfide (WS₂). Our work provides a facile, reproducible and cost-efficient method for the scalable fabrication of high-quality monolayer MoS₂ for versatile applications, such as electronic and optoelectronic devices as well as the membranes for desalination and power generation.