Summary 1. Concern over the impact of invasive species has led to the development of risk assessment methodologies to identify potential invaders and prevent future ecological and economic problems. However, developing a risk assessment tool is challenging because of the difficulties of accurately predicting the outcome of species introductions. 2. In this study, we develop a global risk assessment for birds. We integrate two approaches, generalized linear mixed models (GLMM) and hierarchical tree models, to help identify those introductions with the highest risk of establishment success. 3. Past work has shown that the number of individuals released is the main factor influencing establishment success in animals, a conclusion that was supported in our analyses. Establishment success was also higher for species with broader ecological niches and larger brains relative to body size. These features should increase the likelihood of finding an appropriate niche in the region of introduction. 4. The GLMM and tree model predicted the probability of establishment success of birds in Europe and Australia with high accuracy (over 80% of introductions correctly classified). This highlights that establishment risk can be reasonably assessed with information on general habitat use, brain size and the size of the founder population. When compared with an alternative risk assessment tool based on a qualitative ranking, our quantitative approaches achieved higher accuracy with less information. 5. Synthesis and applications. Quantitative risk assessments based on traits related to establishment success are difficult but feasible, providing a useful tool for guiding preventive polices aimed at mitigating the impact of invasive species.