Device engineering based on the tunable electronic properties of ternary transition metal dichalcogenides has recently gained widespread research interest. In this work, monolayer ternary telluride core/shell structures are synthesized using a one-step chemical vapor deposition process with rapid cooling. The core region is the tellurium-rich WSe2-2x Te2x alloy, while the shell is the tellurium-poor WSe2-2y Te2y alloy. The bandgap of the material is ≈1.45 eV in the core region and ≈1.57 eV in the shell region. The lateral gradient of the bandgap across the monolayer heterostructure allows for the fabrication of heterogeneous transistors and photodetectors. The difference in work function between the core and shell regions leads to a built-in electric field at the heterojunction. As a result, heterogeneous transistors demonstrate a unidirectional conduction and strong photovoltaic effect. The bandgap gradient and high mobility of the ternary telluride core/shell structures provide a unique material platform for novel electronic and photonic devices.