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Realizing the rational control of two-dimensional valleytronics is appealing for potential applications in valleytronic devices. Using density functional theory method, we systematically study the magnetoelectronic coupling properties in ferrovalley/ferroelectricity van der Waals (vdW) heterostructure, ScI2/Ga2STe2. Interestingly, an on/off transition of the valley nature is found for this multiferroic ScI2/Ga2STe2 heterostructure. Under the Ga2STe2-P↑ polarization state, the heterostructure shows a ferromagnetic (FM) semiconducting feature with valley polarization, while it turns out to be FM metal when the ferroelectric (FE) polarization is switched to Ga2STe2-P↓; therefore, a switchable valleytronic device can be realized by altering the FE polarization direction. Furthermore, it is found that such switchable valleytronic behaviors of the ScI2/Ga2STe2 heterostructure can be modulated by applying biaxial strains for both FE polarization directions. The research of nonvolatile electrical control of valley splitting in the two-dimensional ScI2/Ga2STe2 multiferroic heterostructure provides a way for designing all-in-one valleytronic devices. [ABSTRACT FROM AUTHOR]