The U.S. Southwest is projected to experience increasing aridity due to climate change. We quantify the resulting impacts on ambient dust levels and public health using methods consistent with the Environmental Protection Agency's Climate Change Impacts and Risk Analysis framework. We first demonstrate that U.S. Southwest fine (PM2.5) and coarse (PM2.5-10) dust levels are strongly sensitive to variability in the 2-month Standardized Precipitation-Evapotranspiration Index across southwestern North America. We then estimate potential changes in dust levels through 2099 by applying the observed sensitivities to downscaled meteorological output projected by six climate models following an intermediate (Representative Concentration Pathway 4.5, RCP4.5) and a high (RCP8.5) greenhouse gas concentration scenario. By 2080-2099 under RCP8.5 relative to 1986-2005 in the U.S. Southwest: (1) Fine dust levels could increase by 57%, and fine dust-attributable all-cause mortality and hospitalizations could increase by 230% and 360%, respectively; (2) coarse dust levels could increase by 38%, and coarse dust-attributable cardiovascular mortality and asthma emergency department visits could increase by 210% and 88%, respectively; (3) climate-driven changes in dust concentrations can account for 34-47% of these health impacts, with the rest due to increases in population and baseline incidence rates; and (4) economic damages of the health impacts could total $47 billion per year additional to the 1986-2005 value of $13 billion per year. Compared to national-scale climate impacts projected for other U.S. sectors using the Climate Change Impacts and Risk Analysis framework, dust-related mortality ranks fourth behind extreme temperature-related mortality, labor productivity decline, and coastal property loss.