Structural defects are widely regarded as detrimental to the optoelectronic properties of monolayer transition metal dichalcogenides, leading to concerted efforts to eliminate defects via improved materials growth or post-growth passivation. Here, using steady-state and ultrafast optical spectroscopy, supported by ab initio calculations, we demonstrate that sulfur vacancy defects act as exciton traps. Current chemical treatments do not passivate these sites, leading to decreased mobility and trap-limited photoluminescence. We present a generalizable treatment protocol based on the use of passivating agents such as thiols or sulfides in combination with a Lewis acid to passivate sulfur vacancies in monolayer MoS$_2$ and WS$_2$, increasing photoluminescence up to 275 fold, while maintaining mobilities. Our findings suggest a route for simple and rational defect engineering strategies, where the passivating agent varies the electronic properties, thereby allowing the design of new heterostructures.