Climate change and international migration flows are phenomena which attract a great deal of attention from policymakers, researchers and the general public around the globe. Are these two phenomena related? Is migration an adaptation strategy to sudden or gradual changes in climate? In this paper our aim is to investigate whether countries that are affected by climatic anomalies with respect to long-term mean experience, ceteris paribus, larger outmigration flows toward rich OECD countries in the period 1990-2001. Contrarily to the bulk of existing studies we use a macro approach and analyse the determinants of international bilateral migration flows employing an augmented gravity-like equation and test the relevance of climate anomalies with respect to long-term average temperature and precipitation. One important novelty in our approach is the explicit consideration in the empirical analysis of the heterogeneous nature of climate shocks, i.e. positive vs. negative variations of temperature and precipitations; non linear and threshold effects of climate shocks. Our results show that the occurrence of climate anomalies in origin countries might have heterogeneous impacts on cross-border outmigration flows depending on the type and size of the shocks and on certain socio-economic characteristics of the country (level of development, past immigration history, vulnerability of the agricultural sector). In general, countries with a higher level of development and with a growing share of irrigated agricultural land are less sensitive to climate anomalies. Interestingly we find that the existence of a network of established migrants plays a complex role.