Both neurons and glia communicate via diffusible neuromodulatory substances, but the substrates of computation in such neuromodulatory networks are unclear. During behavioral transitions in the larval zebrafish, the neuromodulator norepinephrine drives fast excitation and delayed inhibition of behavior and circuit activity. We find that the inhibitory arm of this feedforward motif is implemented by astroglial purinergic signaling. Neuromodulator imaging, behavioral pharmacology, and perturbations of neurons and astroglia reveal that norepinephrine triggers astroglial release of adenosine triphosphate, extracellular conversion into adenosine, and behavioral suppression through activation of hindbrain neuronal adenosine receptors. This work, along with a companion piece by Lefton and colleagues demonstrating an analogous pathway mediating the effect of norepinephrine on synaptic connectivity in mice, identifies a computational and behavioral role for an evolutionarily conserved astroglial purinergic signaling axis in norepinephrine-mediated behavioral and brain state transitions.