Two-dimensional layered semiconductors present a promising material platform for band-to-band-tunneling devices given their homogeneous band edge steepness due to their atomically flat thickness. Here, we experimentally demonstrate interlayer band-to-band tunneling in vertical MoS2/WSe2van der Waals (vdW) heterostructures using a dual-gate device architecture. The electric potential and carrier concentration of MoS2and WSe2layers are independently controlled by the two symmetric gates. The same device can be gate modulated to behave as either an Esaki diode with negative differential resistance, a backward diode with large reverse bias tunneling current, or a forward rectifying diode with low reverse bias current. Notably, a high gate coupling efficiency of ∼80% is obtained for tuning the interlayer band alignments, arising from weak electrostatic screening by the atomically thin layers. This work presents an advance in the fundamental understanding of the interlayer coupling and electron tunneling in semiconductor vdW heterostructures with important implications toward the design of atomically thin tunnel transistors.