Neuronal activity shapes brain development and refines synaptic connectivity in part through dynamic changes in gene expression. While activity-regulated transcriptional programs have been extensively characterized, the holistic effects of neuronal activity on the full RNA life cycle remain relatively unexplored. Here, we show that neuronal activity influences multiple stages of RNA metabolism in vitro and in vivo. Among these, RNA stability emerges as a previously underappreciated regulator of gene expression, exerting a stronger influence than transcription on total RNA levels for ~10% of activity-dependent genes. We go on to profile 3\'UTR mRNA motifs that are sufficient to modulate activity-dependent mRNA stability and employ machine learning to identify the neuronal-specific RNA-binding protein HuD as a key regulator of activity-dependent mRNA stabilization. We demonstrate that HuD shapes activity-dependent mRNA abundance of hundreds of transcripts in both soma and distal neuronal processes and that neuronal activity drives the reorganization of HuD-interacting proteins, thereby stabilizing HuD-bound mRNAs and directing them into translationally active granules. Finally, we find that many variants associated with autism spectrum disorder (ASD) and other neurodevelopmental disorders disrupt or promote aberrant activity-dependent changes in mRNA stability. These findings reveal mRNA stability as a widespread mechanism of stimulus-responsive gene regulation in neurons with direct implications for the understanding of neurodevelopmental disorders.