Band gap engineering of atomically thin two-dimensional (2D) materials is the key to their applications in nanoelectronics, optoelectronics, and photonics. Here, for the first time, we demonstrate that in the 2D system, by alloying two materials with different band gaps (MoS2 and WS2), tunable band gap can be obtained in the 2D alloys (Mo(1-x)W(x)S(2) monolayers, x = 0-1). Atomic-resolution scanning transmission electron microscopy has revealed random arrangement of Mo and W atoms in the Mo(1-x)W(x)S(2) monolayer alloys. Photoluminescence characterization has shown tunable band gap emission continuously tuned from 1.82 eV (reached at x = 0.20) to 1.99 eV (reached at x = 1). Further, density functional theory calculations have been carried out to understand the composition-dependent electronic structures of Mo(1-x)W(x)S(2) monolayer alloys.