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Climate change is projected to negatively impact biophysical agricultural productivity in much of the world. Actions taken to reduce greenhouse gas emissions and mitigate future climate changes, are thus of central importance for agricultural production. Climate impacts are, however, not unidirectional; some crops in some regions (primarily higher latitudes) are projected to benefit, particularly if increased atmospheric carbon dioxide is assumed to strongly increase crop productivity at large spatial and temporal scales. Climate mitigation measures that are implemented by reducing atmospheric carbon dioxide concentrations lead to reductions both in the strength of climate change and in the benefits of carbon dioxide fertilization. Consequently, analysis of the effects of climate mitigation on agricultural productivity must address not only regions for which mitigation is likely to reduce or even reverse climate damages. There are also regions that are likely to see increased crop yields due to climate change, which may lose these added potentials under mitigation action. Comparing data from the most comprehensive archive of crop yield projections publicly available, we find that climate mitigation leads to overall benefits from avoided damages at the global scale and especially in many regions that are already at risk of food insecurity today. Ignoring controversial carbon dioxide fertilization effects on crop productivity, we find that for the median projection aggressive mitigation could eliminate ~81% of the negative impacts of climate change on biophysical agricultural productivity globally by the end of the century. In this case, the benefits of mitigation typically extend well into temperate regions, but vary by crop and underlying climate model projections. Should large benefits to crop yields from carbon dioxide fertilization be realized, the effects of mitigation become much more mixed, though still positive globally and beneficial in many food insecure countries.