Magnetic reconnection is a fundamental plasma process that plays a critical role not only in energy release in the solar atmosphere, but also in fusion, astrophysical, and other space plasma environments. One of the challenges in explaining solar observations in which reconnection is thought to play a critical role is to account for the transition of the dynamics from a slow quasi-continuous phase to a fast and impulsive energetic burst of much shorter duration. Despite the theoretical progress in identifying mechanisms that might lead to rapid onset, a lack of observations of this transition has left models poorly constrained. High-resolution spectroscopic observations from NASAs Interface Region Imaging Spectrograph (IRIS) now reveal tell-tale signatures of the abrupt transition of reconnection from a slow phase to a fast, impulsive phase during UV bursts or explosive events in the Suns atmosphere. Our observations are consistent with numerical simulations of the plasmoid instability, and provide evidence for the onset of fast reconnection mediated by plasmoids and new opportunities for remote-sensing diagnostics of reconnection mechanisms on the Sun.