The Global Burden of Disease relates premature mortality to a range of causes, including air pollution by ozone and fine particulate matter (PM2.5). Quantifying the role of air pollution has been a challenge, in part due to uncertainty about human exposure to air pollution worldwide. We present results from a global atmospheric chemistry model, combined with population data, country-level health statistics and pollution exposure response functions. We calculate that outdoor air pollution, mostly by PM2.5, leads to about 4.5 million premature deaths/year worldwide, predominantly in Asia (75%). This is three times the rate by HIV/AIDS and malaria together. Contrary to the common view that traffic, industry and power generation are dominant sources, we show that residential energy use (e.g. heating, cooking) is the largest category worldwide due to its prevalence in India and China. Strong control measures are needed to substantially lower morbidity and mortality from air pollution. Clean air is a human right, being fundamental to many sustainable development goals of the United Nations.