Low power consumption in the static and dynamic modes of operation is a key requirement in the development of modern electronics. Tunnel field-effect transistors with direct band-to-band charge tunnelling and steep-subthreshold-slope transfer characteristics offer one potential solution. However, silicon and III–V heterojunction-based tunnel field-effect transistors suffer from low on-current densities and on/off current ratios at sub-60 mV decade–1 operation. Tunnel field-effect transistors based on two-dimensional materials can offer improved electrostatic control and potentially higher on-current densities and on/off ratios. Here we report gate-tunable heterojunction tunnel triodes that are based on van der Waals heterostructures formed from two-dimensional metal selenide and three-dimensional silicon. These triodes exhibit subthreshold slopes as low as 6.4 mV decade–1 and average subthreshold slopes of 34.0 mV decade–1 over four decades of drain current. The devices have a current on/off ratio of approximately 106 and an on-state current density of 0.3 µA µm–1 at a drain bias of –1 V.