Building on substantial tobacco control action over the previous decade, Australia increased the taxes on tobacco by 25% without forewarning on April 30, 2010. Australia then became one of a few countries to pre-announce a series of increases in tobacco taxes, with annual 12·5% increases starting from December, 2013. We aimed to examine the effects of both tax increases on smoking prevalence. By use of survey data from Australians aged 14 years and older in five capital cities, we did an interrupted time-series analysis to model the monthly prevalence of smoking (overall, of factory-made cigarettes [FMC], and of roll-your-own tobacco [RYO]), in the total sample and stratified by socioeconomic status subgroups. We measured outcomes in May, 2001-April, 2010; May, 2010-November, 2013; and December, 2013-April, 2017. The 25% tax increase was associated with immediate (-0·745 percentage points; 95% CI -1·378 to -0·112) and sustained reductions in prevalence (monthly trend -0·023 percentage points; -0·044 to -0·003), which were driven by reductions in the prevalence of smoking of FMC. The prevalence of smoking of RYO increased between May, 2010, and November, 2013, after the 25% tax increase. At the start of the pre-announced annual 12·5% increases, we observed an immediate reduction in smoking (-0·997 percentage points; -1·632 to -0·362), followed by decreasing overall prevalence (monthly trend -0·044 percentage points; -0·063 to -0·026) due to ongoing decreases in the prevalence of FMC smoking and a cessation of increases in the prevalence of smoking of RYO. Immediate decreases in smoking and changing trends in the prevalence of smoking of RYO were most evident among groups with a lower socioeconomic status. Large tax increases are effective in reducing smoking prevalence, both as a single increase without forewarning and as a pre-announced series of increases. However, taxes on tobacco are best structured to apply equally to FMC and RYO products. Tobacco control policies should prohibit price marketing that otherwise erodes the full impact of such tax increases. Cancer Council Victoria.