Climate change and the global spread of invasive species are currently two of the most significant threats to biodiversity worldwide. Yet the role of adaptation in organismal responses to changing climates or in facilitating species invasions is still poorly understood. We conducted a large-scale trans-continental common garden experiment to understand adaptation to spatiotemporal variation in climate in the native and introduced ranges of a cosmopolitan plant species. Individuals from 96 populations of Trifolium repens (white clover) from both its native (Europe) and introduced (North America) ranges were planted into four experimental common gardens located in northern (Uppsala, Sweden) and southern (Montpellier, France) Europe, and northern (Mississauga, Canada) and southern (Louisiana, USA) North America. We recorded plant sexual and clonal fitness in each common garden and assessed whether plants are best adapted to local climates, whether the strength of local adaptation differed between the native and introduced ranges, and whether populations show evidence of rapid adaptation to recent climate change. Results show that white clover is locally adapted, particularly in lower latitude locations, but also that the most prominent bioclimatic drivers of local adaptation differed by latitude. We also found that strong local adaptation was only evident when populations were transplanted into common gardens located in the same range (native or introduced) from which they originated, indicating rapid local adaptation across a large latitudinal gradient has occurred in T. repens populations in less than 400 years since its introduction to North America. However, we do find some evidence of an adaptation lag in the northern common garden in the introduced range, with plants from historically slightly warmer climates exhibiting the greatest fitness. This indicates that despite evidence of local adaptation to historic climatic conditions and rapid local adaptation post-introduction, white clover populations may be evolving more slowly than climate change is occurring.