Two-dimensional materials present a versatile platform for developing steep transistors due to their uniform thickness and sharp band edges. We demonstrate 2D-2D tunneling in a WSe2/SnSe2 van der Waals vertical heterojunction device, where WSe2 is used as the gate controlled p-layer and SnSe2 is the degenerately n-type layer. The van der Waals gap facilitates the regulation of band alignment at the heterojunction, without the necessity of a tunneling barrier. ZrO2 is used as the gate dielectric, allowing the scaling of gate oxide to improve device subthreshold swing. Efficient gate control and clean interfaces yield a subthreshold swing of ∼100 mV/dec for >2 decades of drain current at room temperature, hitherto unobserved in 2D-2D tunneling devices. The subthreshold swing is independent of temperature, which is a clear signature of band-to-band tunneling at the heterojunction. A maximum switching ratio ION/IOFF of 107 is obtained. Negative differential resistance in the forward bias characteristics is observed at 77 K. This work bodes well for the possibilities of two-dimensional materials for the realization of energy-efficient future-generation electronics.