Background: High body-mass index (BMI; defined as 25 kg/m2 or greater) is associated with increased risk of cancer. To inform public health policy and future research, we estimated the global burden of cancer attributable to high BMI in 2012. Methods: In this population-based study, we derived population attributable fractions (PAFs) using relative risks and BMI estimates in adults by age, sex, and country. Assuming a 10-year lag-period between high BMI and cancer occurrence, we calculated PAFs using BMI estimates from 2002 and used GLOBOCAN2012 data to estimate numbers of new cancer cases attributable to high BMI. We also calculated the proportion of cancers that were potentially avoidable had populations maintained their mean BMIs recorded in 1982. We did secondary analyses to test the model and to estimate the effects of hormone replacement therapy (HRT) use and smoking. Findings: Worldwide, we estimate that 481 000 or 3·6% of all new cancer cases in adults (aged 30 years and older after the 10-year lag period) in 2012 were attributable to high BMI. PAFs were greater in women than in men (5·4% vs 1·9%). The burden of attributable cases was higher in countries with very high and high human development indices (HDIs; PAF 5·3% and 4·8%, respectively) than in those with moderate (1·6%) and low HDIs (1·0%). Corpus uteri, postmenopausal breast, and colon cancers accounted for 63·6% of cancers attributable to high BMI. A quarter (about 118-000) of the cancer cases related to high BMI in 2012 could be attributed to the increase in BMI since 1982. Interpretation: These findings emphasise the need for a global effort to abate the increasing numbers of people with high BMI. Assuming that the association between high BMI and cancer is causal, the continuation of current patterns of population weight gain will lead to continuing increases in the future burden of cancer.