There is growing evidence that rapid adaptation to novel environments drives successful establishment and spread of invasive plant species. However, the mechanisms driving trait adaptation, such as selection pressure from novel climate niche envelopes, remain poorly tested at global scales. In this study, we investigated differences in 20 traits (relating to growth, resource acquisition, reproduction, phenology and defence) amongst 14 populations of the herbaceous plant Sonchus oleraceus L. (Asteraceae) across its native (Europe and North Africa) and introduced (Australia and New Zealand) ranges. We compared traits amongst populations grown under standard glasshouse conditions. Introduced S. oleraceus plants seemed to outperform native plants, i.e. possessing higher leaf and stem dry matter content, greater number of leaves and were taller at first flowering stage. Although introduced plants produced fewer seeds, they had a higher germination rate than native plants. We found strong evidence for adaptation along temperature and precipitation gradients for several traits (e.g. shoot height, biomass, leaf and stem dry matter contents increased with minimum temperatures, while germination rate decreased with annual precipitations and temperatures), which suggests that similar selective forces shape populations in both the native and invaded ranges. We detected significant shifts in the relationships (i.e. trade-offs) (i) between plant height and flowering time and (ii) between leaf-stem biomass and grain yield between native and introduced plants, indicating that invasion was associated with changes to life-history dynamics that may confer competitive advantages over native vegetation. Specifically, we found that, at first flowering, introduced plants tended to be taller than native ones and that investment in leaf and stem biomass was greater in introduced than in native plants for equivalent levels of grain yield. Our study has demonstrated that climatic conditions may drive rapid adaption to novel environments in invasive plant species.