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The large exciton binding energy in monolayer transition metal dichalcogenides (TMDs) was determined recently. The robust excitons open a venue to explore the exciton physics such as Bose-Einstein condensation at room temperature. Recent reports further demonstrated the Coulomb engineering via dielectric environment based on a few-layer graphene. However, due to the conducting nature, quenching of optical transitions is often unavoidable. Thus, it is desirable to show the tunability using insulating dielectrics. Here we investigate the impact of dielectric environment on exciton binding energy and quasiparticle bandgap in monolayer WS₂ and WSe₂ by exciton Rydberg spectroscopy. The dielectric constant is systematically varied from κ = 1.49 to 3.82. We found that, with increasing κ, the exciton binding energy and quasiparticle bandgap exhibit significant reductions. We found the model using nonlocally-screened Keldysh potential captures the results very well. Our work validates the applicability of Keldysh model which can be used to design TMD-based optoelectronic devices in different dielectric media.