Using the first-principles method, the structural, electronic, optical and mechanical properties of the vertical and lateral heterostructures based on the boron phosphide (BP) and GaN monolayers, named V-GaN@BP and L-GaN@BP, are investigated systematically. Our results revealed that the band structure of the V-GaN@BP is more sensitive than that of the L-GaN@BP to the strain and the external electric field (E-field). For the V-D-GaN@BP, with the E-field and strain, the band structure not only undergoes a fascinating direct-indirect and semiconductor-metal transition, but also experiences a transition from type-I to type-II. However, the L-NB-GaN@BP maintains a type-II semiconductor with an indirect band gap, though the band gaps can be strongly modulated by applied strain and the E-field. Moreover, the heterostructures are found to be mechanically stable presenting superior optical properties in the visible and UV light range. Consequently, we expect the GaN@BP heterostructures are novel architectures for the future development of efficient optoelectronic devices, due to the selective control of their bandgaps, the excellent optical and mechanical properties.