In plants, a variety of stimuli trigger long-range calcium signals that travel rapidly along the vasculature to distal tissues via poorly understood mechanisms. Here, we use quantitative imaging and analysis to demonstrate that traveling calcium waves are mediated by diffusion and bulk flow of amino acid chemical messengers. We propose that wounding triggers release of amino acids that diffuse locally through the apoplast, activating the calcium-permeable channel GLUTAMATE RECEPTOR-LIKE 3.3 as they pass. Over long distances through the vasculature, the wound-triggered dynamics of a fluorescent tracer show that calcium waves are likely driven by bulk flow of a channel-activating chemical. We observed that multiple stimuli trigger calcium waves with similar dynamics, but calcium waves alone cannot initiate all systemic defense responses, suggesting that mobile chemical messengers are a core component of complex systemic signaling in plants.