Two-dimensional materials and their combined heterostructures have paved the way for numerous next-generation electronic and optoelectronic applications. Herein, we performed first principles calculations to computationally design the MoSe2/WS2 heterostructure and consider its geometric structure, electronic properties and contact behavior, as well as the effects of the electric fields and strain. Our results show that the MoSe2/WS2 heterostructure is energetically, thermodynamically and mechanically stable. Depending on the stacking configurations, the MoSe2/WS2 heterostructure could form type-I or type-II band alignment. The versatility in contact behavior makes the MoSe2/WS2 heterostructure attractive in electronics and optoelectronics. The combination of the MoSe2/WS2 heterostructure also leads to an enhancement in the adsorption efficiency and the carrier mobility compared with the constituent components. More interestingly, our findings demonstrate that the electric field can induce the transition between type-I and type-II band alignments, as evident by the experimental measurement [J. Kistner-Morris, A. Shi, E. Liu, T. Arp, F. Farahmand, T. Taniguchi, K. Watanabe, V. Aji, C. H. Lui and N. Gabor, Nat. Commun., 2024, 15, 4075]. Additionally, we also find that strain can also induce the transition between type-I and type-II band alignments and lead to the transition from semiconductor to metal in the MoSe2/WS2 heterostructure. Our findings prove that the MoSe2/WS2 heterostructure holds significant potential for developing next-generation electronics.