Rationale There is a paucity of large cohort studies examining the association of obstructive sleep apnoea (OSA) with clinical outcomes including all-cause mortality, coronary heart disease (CHD), strokes and chronic kidney disease (CKD). Objectives We hypothesised that a diagnosis of incident OSA is associated with higher risks of these adverse clinical outcomes. Methods, measurements In a nationally representative cohort of over 3 million (n=3 079 514) US veterans (93% male) with baseline estimated glomerular filtration rate (eGFR)≥60 mL/min/1.73 m2, we examined the association between the diagnosis of incident OSA, treated and untreated with CPAP, and: (1) all-cause mortality, (2) incident CHD, (3) incident strokes, (4) incident CKD defined as eGFR<60 mL/min/1.73 m2, and (5) slopes of eGFR. Main results Compared with OSA-negative patients, untreated and treated OSA was associated with 86% higher mortality risk, (adjusted HR and 95% CI 1.86 (1.81 to 1.91) and 35% (1.35 (1.21 to 1.51)), respectively. Similarly, untreated and treated OSA was associated with 3.5 times (3.54 (3.40 to 3.69)) and 3 times (3.06 (2.62 to 3.56)) higher risk of incident CHD; 3.5 times higher risk of incident strokes (3.48 (3.28 to 3.64) and 3.50 (2.92 to 4.19)) for untreated and treated OSA, respectively. The risk of incident CKD was also significantly higher in untreated (2.27 (2.19 to 2.36)) and treated (2.79 (2.48 to 3.13)) patients with OSA. The median (IQR) of the eGFR slope was -0.41 (-2.01 to 0.99), -0.61 (-2.69 to 0.93) and -0.87 (-3.00 to 0.70) mL/min/1.73 m2 in OSA-negative patients, untreated OSA-positive patients and treated OSA-positive patients, respectively. Conclusions In this large and contemporary cohort of more than 3 million US veterans, a diagnosis of incident OSA was associated with higher mortality, incident CHD, stroke and CKD and with faster kidney function decline.