Invasions are multistage processes and the performance of a species at different stages depends on socio-economic, biogeographical, ecological and evolutionary factors. Most studies addressing the factors that determine invasion success focus on one particular stage, usually by examining data on introduced species that have successfully naturalized, whereas species that fail to naturalize are often not considered. In this study, we examined naturalization success (whether a species escaped from cultivation and became naturalized in the wild) and occupancy (the number of grid cells of 6′ longitude×10′ latitude in which it is recorded) of up to 8018 ornamental plant species introduced into botanical gardens in Germany. Data on these introductions were extracted from the SYSTAX database (Information System of German Botanical Gardens), information on successful naturalization in Germany from the BiolFlor database and data on species traits from SYSTAX and the European Garden Flora. The effect of propagule pressure, biogeography, winter hardiness, life strategy, morphology and genetic variability on the probability of naturalization and the number of grid cells occupied was tested using regression models. The influence of phylogenetic dependence was considered within simple single variable models as a nested random effect. All traits that appeared significant in these simple models were combined in a multivariable model. The simplified multivariable model revealed an increasing probability of naturalization for species with a higher winter hardiness, a wider native range and a higher planting frequency in botanical gardens (Nagelkerke-R2 of 0.196). Moreover, interactions between plant height and planting frequency and between growth form and winter hardiness also affected the probability of naturalization. The number of grid cells occupied was best explained by the winter hardiness (pseudo-R2 of 0.61). The stratified pre-selection of ornamental plants by gardeners may hold the key to their successful escape from cultivation and subsequent naturalization.