To avoid the most dangerous consequences of anthropogenic climate change, the Paris Agreement provides a clear and agreed climate mitigation target of stabilizing global surface warming to under 2.0 °C above preindustrial, and preferably closer to 1.5 °C. However, policy makers do not currently know exactly what carbon emissions pathways to follow to stabilize warming below these agreed targets, because there is large uncertainty in future temperature rise for any given pathway. This large uncertainty makes it difficult for a cautious policy maker to avoid either: (1) allowing warming to exceed the agreed target; or (2) cutting global emissions more than is required to satisfy the agreed target, and their associated societal costs. This study presents a novel Adjusting Mitigation Pathway (AMP) approach to restrict future warming to policy-driven targets, in which future emissions reductions are not fully determined now but respond to future surface warming each decade in a self-adjusting manner. A large ensemble of Earth system model simulations, constrained by geological and historical observations of past climate change, demonstrates our self-adjusting mitigation approach for a range of climate stabilization targets ranging from 1.5 to 4.5 °C, and generates AMP scenarios up to year 2300 for surface warming, carbon emissions, atmospheric CO2, global mean sea level, and surface ocean acidification. We find that lower 21st century warming targets will significantly reduce ocean acidification this century, and will avoid up to 4m of sea-level rise by year 2300 relative to a high-end scenario.