An important factor influencing whether or not a non-native plant species becomes invasive is the climate in the area of introduction. To become naturalised in the new range, a species must either be climatically pre-adapted (climate matching), have a high phenotypic plasticity, or be able to adapt genetically, which in the latter case may take many generations. Furthermore, patterns of successful establishment across species might vary with habitat context. To address the interaction of these factors on non-native species richness, we recorded the presence of non-native annual plant species along an altitudinal gradient on Tenerife (Canary Islands, Spain). We compared the distributions of species differing in bioclimatic origin (Mediterranean and temperate) and time since introduction (old and recent introductions), and compared richness patterns of these groups in anthropogenic and natural habitats. Non-native species richness increased strongly from lowlands to mid-altitudes, but dropped sharply at the transition from anthropogenic to natural habitats, and thereafter declined with altitude in the natural habitat. This pattern indicates that the altitude effects reflected changes in both climate and habitat context. Mediterranean and temperate species were distributed similarly along the altitudinal gradient, and we found no effect of bioclimatic origin on species distributions. As almost all species present at the highest sites also occurred in the lowlands, we conclude that most species were introduced to lowland sites and were therefore pre-adapted to those climatic conditions (lowland introduction filter). The altitudinal ranges of species tended to increase with time since introduction, and the species reaching the highest altitudes were mostly old introductions. This effect of time was more pronounced among Mediterranean than temperate species. Thus, while climatic pre-adaptation is important for establishment along this altitudinal gradient, species tend to extend their altitudinal range with time.