Why can alien species succeed in environments to which they have had no opportunity to adapt and even become more abundant than many native species? Ecological theory suggests two main possible answers for this paradox: competitive superiority of exotic species over native species and opportunistic use of ecological opportunities derived from human activities. We tested these hypotheses in birds combining field observations and experiments along gradients of urbanization in New South Wales (Australia). Five exotic species attained densities in the study area comparable to those of the most abundant native species, and hence provided a case for the invasion paradox. The success of these alien birds was not primarily associated with a competitive superiority over native species: the most successful invaders were smaller and less aggressive than their main native competitors, and were generally excluded from artificially created food patches where competition was high. More importantly, exotic birds were primarily restricted to urban environments, where the diversity and abundance of native species were low. This finding agrees with previous studies and indicates that exotic and native species rarely interact in nature. Observations and experiments in the field revealed that the few native species that exploit the most urbanized environments tended to be opportunistic foragers, adaptations that should facilitate survival in places where disturbances by humans are frequent and natural vegetation has been replaced by man-made structures. Successful invaders also shared these features, suggesting that their success is not a paradox but can be explained by their capacity to exploit ecological opportunities that most native species rarely use.