ACE inhibitors (ACEIs) are commonly prescribed for hypertension, a global risk factor for cardiovascular disease. Their primary side effect is a dry cough which affects 5-35% of users. As clinical guidelines recommend switching those experiencing cough to an angiotensin-II receptor blocker, we have used this switch as a proxy for ACEI-induced cough. Through a two-stage multi-ancestry genome-wide association study, including up to 7,030 cases and 39,921 controls, we identify five independent genome-wide significant associations implicating six protein-coding genes, including INHBC, KCNIP4, NTSR1 and PREP which encode proteins involved in the nervous system. We also observe genetic overlap between ACEI-induced cough and chronic dry cough through genetic correlation and phenome-wide association studies. In line with existing hypotheses, our findings suggest a neurological basis for the pathology of ACEI-induced cough, particularly the role of proinflammatory mediators in sensory airway sensitivity and cough reflex modulation, and shared biological mechanisms with chronic dry cough.