While there is considerable interest in understanding the climate–migration relationship, particularly in the context of concerns about global climatic change, little is known about its underlying mechanisms. In the paper, we combine a rich panel data on annual bilateral international migration flows with an extensive data on climate variability across the countries to investigate in-depth the climate–migration link. We find a positive and statistically significant relationship between temperature and international outmigration only in the most agriculture-dependent countries, consistent with the widely documented adverse impact of temperature on agricultural productivity. Further, the temperature–migration relationship is nonlinear and resembles the nonlinear temperature–yield relationship. In addition, migration flows to current major destinations are especially temperature-sensitive. Policies to address issues related to climate-induced international migration would be more efficient if focused on the agriculture-dependent countries and especially people in those countries whose livelihoods depend on agriculture. •We examine the relationship between climate variability and international migration.•We use an annual bilateral international migration data set for 1980–2010.•Temperature induces international outmigration only from agricultural countries.•Migration flows to current major destinations are especially temperature-sensitive.