Striatal dopamine encodes reward, with recent work showing that dopamine release occurs in spatiotemporal waves. However, the mechanism of dopamine waves is unknown. Here we report that acetylcholine release in mouse striatum also exhibits wave activity, and that the spatial scale of striatal dopamine release is extended by nicotinic acetylcholine receptors. Based on these findings, and on our demonstration that single cholinergic interneurons can induce dopamine release, we hypothesized that the local reciprocal interaction between cholinergic interneurons and dopamine axons suffices to drive endogenous traveling waves. We show that the morphological and physiological properties of cholinergic interneuron – dopamine axon interactions can be modeled as a reaction-diffusion system that gives rise to traveling waves. Analytically-tractable versions of the model show that the structure and the nature of propagation of acetylcholine and dopamine traveling waves depend on their coupling, and that traveling waves can give rise to empirically observed correlations between these signals. Thus, our study provides evidence for striatal acetylcholine waves in vivo, and proposes a testable theoretical framework that predicts that the observed dopamine and acetylcholine waves are strongly coupled phenomena.