Semiconducting monolayers of transition metal dichalcogenides (TMDs) are considered as emergent materials for nanodevices and optoelectronic applications. The low-frequency electrical noise of TMD-based devices is much higher than Si and other conventional semiconductors. The reduction of this noise along with control of the Ohmic contact and carrier concentration of the such devices remain major challenges. Here, the low-frequency (1/f) noise and transport properties of chemical-vapor-deposition-grown MoS2 are presented. The high mobility of 20–40 cm2 V−1 s−1 of the monolayer devices is highly reproducible. Reliable methods to induce Ohmic contact and to tune carrier density over a wide range of 1011–1014 cm−2 are presented to study the fundamental mechanism of the 1/f noise. The noise performance in the high carrier concentration regime is explored for the first time with Ohmic contact of the devices and ideal sample quality. A significant reduction of the noise figure of merit is achievable in the high-density regime. Polymer electrolyte encapsulation provides a practical method to effectively tune carrier density and engineer surface trap states of the monolayer TMDs, which would be helpful for practical applications of 2D atomic layers in nanoelectronics and photonics.