Migration and climate change are two of the most important challenges the world currently faces. They are connected as climate change may stimulate or hinder migration. One of the sectors strongly affected by climate change is agriculture, which is the source of income for most of the world's poor. Climate change may affect agricultural productivity and hence migration because of its impact on average temperatures and rainfall and because it increases the frequency and intensity of weather shocks. In this paper we use data on 108 countries from 1960 to 2010 to analyze the relationship between weather variations, changes in agricultural productivity and international migration. We find that negative shocks to agricultural productivity caused by climate fluctuations significantly increase emigration from developing countries, an especially strong impact in poor countries but less so in middle income countries. These results are robust to the definitions of the poor country sample, and to several checks and alternative explanations suggested by the literature. Importantly, our results point to a causal interpretation of the agricultural channel to explain the climate change-migration nexus.