Ataxia‐telangiectasia (A‐T) is a genetic disorder caused by the lack of functional ATM kinase. A‐T is characterized by chronic inflammation, neurodegeneration and premature ageing features that are associated with increased genome instability, nuclear shape alterations, micronuclei accumulation, neuronal defects and premature entry into cellular senescence. The causal relationship between the detrimental inflammatory signature and the neurological deficiencies of A‐T remains elusive. Here, we utilize human pluripotent stem cell‐derived cortical brain organoids to study A‐T neuropathology. Mechanistically, we show that the cGAS‐STING pathway is required for the recognition of micronuclei and induction of a senescence‐associated secretory phenotype (SASP) in A‐T olfactory neurosphere‐derived cells and brain organoids. We further demonstrate that cGAS and STING inhibition effectively suppresses self‐DNA‐triggered SASP expression in A‐T brain organoids, inhibits astrocyte senescence and neurodegeneration, and ameliorates A‐T brain organoid neuropathology. Our study thus reveals that increased cGAS and STING activity is an important contributor to chronic inflammation and premature senescence in the central nervous system of A‐T and constitutes a novel therapeutic target for treating neuropathology in A‐T patients. Aguado et al. show that senescent astrocytes upregulate detrimental pro‐inflammatory SASP factors in a cGAS/STING‐dependant manner that promote accelerated ageing in brain organoids of ataxia‐telangiectasia. Pharmacological interventions in these organoids with cGAS and STING inhibitors reduce astrocyte senescence and the SASP, and consequently, improve neuronal activity and survival.