Single layers of hexagonal boron nitride (h-BN) and silicene are brought together to form h-BN/silicene van der Waals (vdW) heterostructures. The effects of external electric fields and compressive strain on their structural and electronic properties are systematically studied through first principles calculations. Two silicene phases are considered: the low-buckled Si(LB) and the dumbbell-like Si(DB). They show exciting new properties as compared to the isolated layers, such as a tunable band gap that depends on the interlayer distance and is dictated by the charge transfer and orbital hybridization between h-BN and silicene, especially in the case of Si(LB). The electric field also increases the band gap in h-BN/Si(DB) and causes an asymmetric charge rearrangement in h-BN/Si(LB). Remarkably, we found a great potential of h-BN layers to function as substrates for silicene, enhancing both the strain and electric field effects on its electronic properties. These results contribute to a more detailed understanding of h-BN/Si 2D-based materials, highlighting promising possibilities in low-dimensional electronics.