Two-dimensional/two-dimensional (2D/2D) heterojunctions form one of the most versatile technological solutions for building tunneling field effect transistors because of the sharp and potentially clean interfaces resulting from van der Waals assembly. Several evidences of room temperature band-to-band tunneling (BTBT) have been recently reported, but only few tunneling devices have been proven to break the Boltzmann limit of the minimum subthreshold slope, 60 mV per decade at 300 K. Here, we report the fabrication and characterization of a vertical p-type Tunnel FET (TFET) co-integrated on the same flake with a p-type MOSFET in a WSe2/SnSe2 material system platform. Due to the selected beneficial band alignment and to a van der Waals device architecture having an excellent heterostructure 2D-2D interface, the reported tunneling devices have a sub-thermionic point swing, reaching a value of 35 mV per decade, while maintaining excellent ON/OFF current ratio in excess of 10(5) at V-DS = 500 mV. The TFET characteristics are directly compared with the ones of a WSe2 MOSFET realized on the very same flake used in the heterojunction. The tunneling device clearly outperforms the 2D MOSFET in the subthreshold region, crossing its characteristic over several orders of magnitude of the output current and providing better digital and analog figures of merit.