Updating behavior based on feedback from the environment is a crucial means by which organisms learn and develop optimal behavioral strategies1-3. Norepinephrine (NE) release from the locus coeruleus (LC) has been shown to mediate learned behaviors4-6 such that in a task with graded stimulus uncertainty and performance, a high level of NE released after an unexpected outcome causes improvement in subsequent behavior7. Yet, how the transient activity of LC-NE neurons, lasting tens of milliseconds, influences behavior several seconds later, is unclear. Here, we show that NE acts directly on cortical astrocytes via Adra1a adrenergic receptors to elicit sustained increases in intracellular calcium. Chemogenetic blockade of astrocytic calcium elevation prevents the improvement in behavioral performance. NE-activated calcium invokes purinergic pathways in cortical astrocytes that signal to neurons; pathway-specific astrocyte gene expression is altered in mice trained on the task, and blocking neuronal adenosine-sensitive A1 receptors also prevents post-reinforcement behavioral gain. Finally, blocking either astrocyte calcium dynamics or A1 receptors alters encoding of the task in prefrontal cortex neurons, preventing the post-reinforcement change in discriminability of rewarded and unrewarded stimuli underlying behavioral improvement. Together, these data demonstrate that astrocytes, rather than indirectly reflecting neuronal drive, play a direct, instrumental role in representing task-relevant information and signaling to neurons to mediate a fundamental component of learning in the brain.