BACKGROUND: The benefits to adults who quit smoking increase over time as former smokers live longer, healthier lives. Youth who never smoke will benefit for decades. Thus, the long-term population effects of tobacco prevention and control policies may be substantial. Yet they are rarely quantified in evaluations of state tobacco control programmes. METHODS: Using a microsimulation model, we predicted the benefits to Minnesotans from 2018 to 2037 of having reduced cigarette smoking prevalence from 1998 to 2017. We first simulated the health and economic harms of tobacco that would have occurred had smoking prevalence stayed at 1997 levels. The harms produced by that scenario were then compared with harms in scenarios with smoking declining at observed rates from 1998 to 2017 and either expected declines from 2018 to 2037 or a greater decline to 5% prevalence in 2037. RESULTS: With expected smoking prevalence decreases from 2018 to 2037, Minnesotans will experience 12 298 fewer cancers, 72 208 fewer hospitalisations for cardiovascular disease and diabetes, 31 913 fewer respiratory disease hospitalisations, 14 063 fewer smoking-attributable deaths, $10.2 billion less in smoking-attributable medical expenditures and $9.4 billion in productivity gains than if prevalence had stayed at 1997 levels. These gains are two to four times greater than for the previous 20 years, and would be about 15% higher if Minnesota achieves a 5% adult prevalence rate by 2037. CONCLUSIONS: The tobacco control measures implemented from 1998 to 2017 will produce accelerated benefits during 2018-2037 if modest progress in tobacco prevalence rates is maintained.