Recent research suggests that climate variability and change significantly affect forced migration, within and across borders. Yet, migration is also informed by a range of non-climatic factors, and current assessments are impeded by a poor understanding of the relative importance of these determinants. Here, we evaluate the eligibility of climatic conditions relative to economic, political, and contextual factors for predicting bilateral asylum migration to the European Union—form of forced migration that has been causally linked to climate variability. Results from a machine-learning prediction framework reveal that drought and temperature anomalies are weak predictors of asylum migration, challenging simplistic notions of climate-driven refugee flows. Instead, core contextual characteristics shape latent migration potential whereas political violence and repression are the most powerful predictors of time-varying migration flows. Future asylum migration flows are likely to respond much more to political changes in vulnerable societies than to climate change.