The Red-whiskered bulbul is a very successful invasive bird species. Morphological differences have been reported among individuals inhabiting the humid and dry coasts of Reunion Island, in a 30-year-old population. This suggests a capacity for rapid local adaptation which could explain the general invasive success of this species. However, the origin and invasion history of this population is unknown. It is therefore not possible to establish with certainty the cause of these morphological differences. Here, we investigated the invasion history of populations of Red-whiskered bulbul established on Reunion Island, Mauritius and Oahu (three geographically similar tropical islands) to assess the link between invasion history and morphological changes in these populations. We first assessed the source(s) of the invasive populations. We then compared the morphology of the individuals between the invasive and native populations, and between the dry and humid coasts of invaded islands. Finally, we inferred the invasion history of the invasive populations to investigate the role of neutral processes (e.g. founder effect and drift) on morphology. We found that the invasive populations have a similar origin and that the morphology of the individuals in these populations has diverged in a similar way from the native range, suggesting a convergent adaptation to tropical islands. Like on Reunion, we found differences in morphology between the dry and humid coasts on Mauritius. These morphological differences can be explained by invasion history on Reunion but not on Mauritius. Both neutral evolution and adaptation thus shape the morphology of invasive Red-whiskered bulbuls.