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Climate projections show Australia becoming significantly warmer during the 21st century, and precipitation decreasing over much of the continent. Such changes are conventionally considered to increase wildfire risk. Nevertheless, we show that burnt area increases in southern Australia, but decreases in northern Australia. Overall the projected increase in fire is small (0.72-1.31% of land area, depending on the climate scenario used), and does not cause a decrease in carbon storage. In fact, carbon storage increases by 3.7-5.6 Pg C (depending on the climate scenario used). Using a process-based model of vegetation dynamics, vegetation-fire interactions and carbon cycling, we show increased fire promotes a shift to more fire-adapted trees in wooded areas and their encroachment into grasslands, with an overall increase in forested area of 3.9-11.9%. Both changes increase carbon uptake and storage. The increase in woody vegetation increases the amount of coarse litter, which decays more slowly than fine litter hence leading to a relative reduction in overall heterotrophic respiration, further reducing carbon losses. Direct CO2 effects increase woody cover, water-use efficiency and productivity, such that carbon storage is increased by 8.5-14.8 Pg C compared to simulations in which CO2 is held constant at modern values. CO2 effects tend to increase burnt area, fire fluxes and therefore carbon losses in arid areas, but increase vegetation density and reduce burnt area in wooded areas.