On the basis of first-principles and cluster expansion calculations, we propose an effective approach to realize monolayer transition metal dichalcogenides with sizable band gaps and improved optoelectronic performance. We show that monolayer Mo(S1–xSex)2 and Mo1–yWyS2 with x = 1/3, 2/3 and y = 1/3, 1/2, 2/3 are stable according to phonon calculations and realize 1T′ or 1T″ phases. The transition barriers from the 2H phase are lower than for monolayer MoS2, implying that the 1T′ or 1T″ phases can be achieved experimentally. Furthermore, it turns out that the 1T″ monolayer alloys with x = 1/3, 2/3 and y = 1/3, 2/3 are semiconductors with band gaps larger than 1 eV, due to trimerization. The visible light absorption and carrier mobility are strongly improved as compared to 2H monolayer MoS2, MoSe2, and WS2. Thus, the 1T″ monolayer alloys have the potential to expand the applications of transition metal dichalcogenides, for example, in solar cells.