Background: People with Down syndrome (DS) show clinical signs of accelerated ageing. Causative mechanisms remain unknown and hypotheses range from the (essentially untreatable) amplified-chromosomal-instability explanation, to potential actions of individual supernumerary chromosome-21 genes. The latter explanation could open a route to therapeutic amelioration if the specific over-acting genes could be identified and their action toned-down. Methods: Biological age was estimated through patterns of sugar molecules attached to plasma immunoglobulin-G (IgG-glycans, an established "biological-ageing-clock") in n = 246 individuals with DS from three European populations, clinically characterised for the presence of co-morbidities, and compared to n = 256 age-, sex- and demography-matched healthy controls. Isogenic human induced pluripotent stem cell (hiPSCs) models of full and partial trisomy-21 with CRISPR-Cas9 gene editing and two kinase inhibitors were studied prior and after differentiation to cerebral organoids. Findings: Biological age in adults with DS is (on average) 18.4-19.1 years older than in chronological-age-matched controls independent of co-morbidities, and this shift remains constant throughout lifespan. Changes are detectable from early childhood, and do not require a supernumerary chromosome, but are seen in segmental duplication of only 31 genes, along with increased DNA damage and decreased levels of LaminB1 in nucleated blood cells. We demonstrate that these cell-autonomous phenotypes can be gene-dose-modelled and pharmacologically corrected in hiPSCs and derived cerebral organoids. Using isogenic hiPSC models we show that chromosome-21 gene DYRK1A overdose is sufficient and necessary to cause excess unrepaired DNA damage. Interpretation: Explanation of hitherto observed accelerated ageing in DS as a developmental progeroid syndrome driven by DYRK1A overdose provides a target for early pharmacological preventative intervention strategies.