Adaptation is the central feature and leading explanation for the evolutionary diversification of life. Adaptation is also notoriously difficult to study in nature, owing to its complexity and logistically prohibitive timescale. Here, we leverage extensive contemporary and historical collections of Ambrosia artemisiifolia-an aggressively invasive weed and primary cause of pollen-induced hayfever-to track the phenotypic and genetic causes of recent local adaptation across its native and invasive ranges in North America and Europe, respectively. Large haploblocks-indicative of chromosomal inversions-contain a disproportionate share (26%) of genomic regions conferring parallel adaptation to local climates between ranges, are associated with rapidly adapting traits, and exhibit dramatic frequency shifts over space and time. These results highlight the importance of large-effect standing variants in rapid adaptation, which have been critical to A. artemisiifolia's global spread across vast climatic gradients.