BACKGROUND: The contribution of modifiable risk factors to the increasing global and regional burden of stroke is unclear, but knowledge about this contribution is crucial for informing stroke prevention strategies. We used data from the Global Burden of Disease Study 2013 (GBD 2013) to estimate the population-attributable fraction (PAF) of stroke-related disability-adjusted life-years (DALYs) associated with potentially modifiable environmental, occupational, behavioural, physiological, and metabolic risk factors in different age and sex groups worldwide and in high-income countries and low-income and middle-income countries, from 1990 to 2013. METHODS: We used data on stroke-related DALYs, risk factors, and PAF from the GBD 2013 Study to estimate the burden of stroke by age and sex (with corresponding 95% uncertainty intervals [UI]) in 188 countries, as measured with stroke-related DALYs in 1990 and 2013. We evaluated attributable DALYs for 17 risk factors (air pollution and environmental, dietary, physical activity, tobacco smoke, and physiological) and six clusters of risk factors by use of three inputs: risk factor exposure, relative risks, and the theoretical minimum risk exposure level. For most risk factors, we synthesised data for exposure with a Bayesian meta-regression method (DisMod-MR) or spatial-temporal Gaussian process regression. We based relative risks on meta-regressions of published cohort and intervention studies. Attributable burden for clusters of risks and all risks combined took into account evidence on the mediation of some risks, such as high body-mass index (BMI), through other risks, such as high systolic blood pressure (SBP) and high total cholesterol. FINDINGS: Globally, 90·5% (95% UI 88·5-92·2) of the stroke burden (as measured in DALYs) was attributable to the modifiable risk factors analysed, including 74·2% (95% UI 70·7-76·7) due to behavioural factors (smoking, poor diet, and low physical activity). Clusters of metabolic factors (high SBP, high BMI, high fasting plasma glucose, high total cholesterol, and low glomerular filtration rate; 72·4%, 95% UI 70·2-73·5) and environmental factors (air pollution and lead exposure; 33·4%, 95% UI 32·4-34·3) were the second and third largest contributors to DALYs. Globally, 29·2% (95% UI 28·2-29·6) of the burden of stroke was attributed to air pollution. Although globally there were no significant differences between sexes in the proportion of stroke burden due to behavioural, environmental, and metabolic risk clusters, in the low-income and middle-income countries, the PAF of behavioural risk clusters in males was greater than in females. The PAF of all risk factors increased from 1990 to 2013 (except for second-hand smoking and household air pollution from solid fuels) and varied significantly between countries. INTERPRETATION: Our results suggest that more than 90% of the stroke burden is attributable to modifiable risk factors, and achieving control of behavioural and metabolic risk factors could avert more than three-quarters of the global stroke burden. Air pollution has emerged as a significant contributor to global stroke burden, especially in low-income and middle-income countries, and therefore reducing exposure to air pollution should be one of the main priorities to reduce stroke burden in these countries. FUNDING: Bill & Melinda Gates Foundation, American Heart Association, US National Heart, Lung, and Blood Institute, Columbia University, Health Research Council of New Zealand, Brain Research New Zealand Centre of Research Excellence, and National Science Challenge, Ministry of Business, Innovation and Employment of New Zealand.