Vanadium dioxide (VO2) shows promise as a building block of switching and sensing devices because it undergoes an abrupt metal-insulator transition (MIT) near room temperature, where the electrical resistivity changes by orders of magnitude. A challenge for versatile applications of VO2 is to control the MIT by gating in the field-effect device geometry. Here, we demonstrate a gate-tunable abrupt switching device based on a VO2 microwire that is monolithically integrated with a two-dimensional (2D) tungsten diselenide (WSe2) semiconductor by van der Waals stacking. We fabricated the WSe2 transistor using the VO2 wire as the drain contact, titanium as the source contact, and hexagonal boron nitride as the gate dielectric. The WSe2 transistor was observed to show ambipolar transport, with higher conductivity in the electron branch. The electron current increases continuously with gate voltage below the critical temperature of the MIT of VO2. Near the critical temperature, the current shows an abrupt and discontinuous jump at a given gate voltage, indicating that the MIT in the contacting VO2 is thermally induced by gate-mediated self-heating. Our results have paved the way for the development of VO2-based gate-tunable devices by the van der Waals stacking of 2D semiconductors, with great potential for electronic and photonic applications.