The Murchison Widefield Array (MWA) is an electronically steered low frequency ($<300$\,MHz) radio interferometer, with a `slew' time less than 8seconds. Low frequency ($\sim 100$\,MHz) radio telescopes are ideally suited for rapid-response follow-up of transients due to their large field of view, the inverted spectrum of coherent emission, and the fact that the dispersion delay between a 1GHz and 100MHz pulse is on the order of $1-10$\,min for dispersion measures of $100-2000$\,pc/cm$^3$. The MWA has previously been used to provide fast follow up for transient events including gamma-ray bursts, fast radio bursts, and gravitational waves, using systems that respond to gamma-ray coordinates network (GCN) packet-based notifications. We describe a system for automatically triggering MWA observations of such events, based on VOEvent triggers, which is more flexible, capable, and accurate than previous systems. The system can respond to external multi-messenger triggers, which makes it well-suited to searching for prompt coherent radio emission from gamma-ray bursts, the study of fast radio bursts and gravitational waves, single pulse studies of pulsars, and rapid follow-up of high-energy superflares from flare stars. The new triggering system has the capability to trigger observations in both the regular correlator mode (limited to $\geq 0.5$\,s integrations) or using the Voltage Capture System (VCS, $0.1$\,ms integration) of the MWA, and represents a new mode of operation for the MWA. The upgraded standard correlator triggering capability has been in use since MWA observing semester 2018B (July-Dec 2018), and the VCS and buffered mode triggers will become available for observing in a future semester.