Two-dimensional (2D) layered transition metal dichalcogenides (TMDs) have recently emerged as a new class of atomically thin semiconductors for diverse electronic, optoelectronic, and valleytronic applications. To explore the full potential of these 2D semiconductors requires a precise control of their band gap and electronic properties, which represents a significant challenge in 2D material systems. Here we demonstrate a systematic control of the electronic properties of 2D-TMDs by creating mixed alloys of the intrinsically p-type WSe2 and intrinsically n-type WS2 with variable alloy compositions. We show that a series of WS2xSe2-2x alloy nanosheets can be synthesized with fully tunable chemical compositions and optical properties. Electrical transport studies using back-gated field effect transistors demonstrate that charge carrier types and threshold voltages of the alloy nanosheet transistors can be systematically tuned by adjusting the alloy composition. A highly p-type behavior is observed in selenium-rich alloy, which gradually shifts to lightly p-type, and then switches to lightly n-type characteristics with the increasing sulfur atomic ratio, and eventually evolves into highly n-doped semiconductors in sulfur-rich alloys. The synthesis of WS2xSe2-2x nanosheets with tunable optical and electronic properties represents a critical step toward rational design of 2D electronics with tailored spectral responses and device characteristics.