Two-dimensional (2D) van der Waals (vdW) heterostructures are considered as promising candidates for realizing multifunctional applications, including photodetectors, field effect transistors and solar cells. In this work, we performed first-principles calculations to design a 2D vdW MoTe2/MoS2 heterostructure and investigate its electronic properties, contact types and the impact of an electric field and in-plane biaxial strain. We find that the MoTe2/MoS2 heterostructure is predicted to be structurally, thermally and mechanically stable. It is obvious that the weak vdW interactions are mainly dominated at the interface of the MoTe2/MoS2 heterostructure and thus it can be synthesized in recent experiments by the transfer method or chemical vapor deposition. The construction of the vdW MoTe2/MoS2 heterostructure forms a staggered type II band alignment, effectively separating the electrons and holes at the interface and thereby extending the carrier lifetime. Interestingly, the electronic properties and contact types of the type II vdW MoTe2/MoS2 heterostructure can be tailored under the application of external conditions, including an electric field and in-plane biaxial strain. The semiconductor-semimetal-metal transition and type II-type I conversion can be achieved in the vdW MoTe2/MoS2 heterostructure. Our findings underscore the potential of the vdW MoTe2/MoS2 heterostructure for the design and fabrication of multifunctional applications, including electronics and optoelectronics.