Severe and persistent disruptions to sleep and circadian rhythms are common features of people with opioid use disorder (OUD). Preclinical findings suggest altered molecular rhythms in the brain are involved in opioid reward and dependence. However, whether molecular rhythms are disrupted in brains of people with OUD remained an open question, critical to understanding the role of circadian rhythms in opioid addiction. We previously used subjects' times of death (TOD) as a marker of time of day to investigate transcriptional rhythm alterations in psychiatric disorders. Using TOD and RNA sequencing, we discovered rhythmic transcripts in both the dorsolateral prefrontal cortex (DLPFC) and nucleus accumbens (NAc), key brain areas involved in opioid addiction, were largely distinct between OUD and unaffected comparison subjects. Further, fewer rhythmic transcripts were identified in DLPFC of OUD subjects compared to unaffected subjects, but nearly double the number of rhythmic transcripts were found in the NAc of OUD subjects. In OUD, rhythmic transcripts in the NAc peaked either in the evening or near sunrise, and were associated with dopamine, opioid, and GABAergic neurotransmission. Co-expression network analysis identified several OUD-specific modules in the NAc, enriched for transcripts involved in the modulation of dopamine and GABA synapses, including glutamatergic signaling and extracellular matrices. Integrative analyses with human GWAS revealed that rhythmic transcripts in DLPFC and NAc were enriched for genomic loci associated with sleep duration and insomnia. Overall, our results connect transcriptional rhythm changes in dopamine, opioid, and GABAergic synaptic signaling in human brain to sleep-related phenotypes and OUD.