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Brain size relative to body size varies considerably among animals, but the ecological consequences of that variation remain poorly understood. Plausibly, larger brains confer increased behavioural flexibility, and an ability to respond to novel challenges. In keeping with that hypothesis, successful invasive species of birds and mammals that flourish after translocation to a new area tend to have larger brains than do unsuccessful invaders. We found the same pattern in ectothermic terrestrial vertebrates. Brain size relative to body size was larger in species of amphibians and reptiles reported to be successful invaders, compared to species that failed to thrive after translocation to new sites. This pattern was found in six of seven global biogeographic realms; the exception (where relatively larger brains did not facilitate invasion success) was Australasia. Establishment success was also higher in amphibian and reptile families with larger relative brain sizes. Future work could usefully explore whether invasion success is differentially associated with enlargement of specific parts of the brain (as predicted by the functional role of the forebrain in promoting behavioural flexibility), or with a general size increase (suggesting that invasion success is facilitated by enhanced perceptual and motor skills, as well as cognitive ability).