Cyclic GMP-AMP synthase (cGAS) senses aberrant DNA during infection, cancer and inflammatory disease, and initiates potent innate immune responses through the synthesis of 2′3′-cyclic GMP-AMP (cGAMP)1–7. The indiscriminate activity of cGAS towards DNA demands tight regulatory mechanisms that are necessary to maintain cell and tissue homeostasis under normal conditions. Inside the cell nucleus, anchoring to nucleosomes and competition with chromatin architectural proteins jointly prohibit cGAS activation by genomic DNA8–15. However, the fate of nuclear cGAS and its role in cell physiology remains unclear. Here we show that the ubiquitin proteasomal system (UPS) degrades nuclear cGAS in cycling cells. We identify SPSB3 as the cGAS-targeting substrate receptor that associates with the cullin–RING ubiquitin ligase 5 (CRL5) complex to ligate ubiquitin onto nuclear cGAS. A cryo-electron microscopy structure of nucleosome-bound cGAS in a complex