Invasive species threaten biodiversity, cause environmental damage, and negatively impact society. While invasion genetics has a history spanning several decades, recent advances in genomics and bioinformatics have enabled an unprecedented toolkit for studies of invasion biology. Natural history collections, including herbaria, allow comparisons of genomic diversity, phenology, and trait variation over both space and time for invasive species, allowing researchers to track population dynamics, genetic diversity, and evidence for adaptive evolution. Recent methodological progress in low-coverage genome analysis is providing genome-scale resolution in myriad organisms, including invasive species, and is quickly becoming a feasible reality for researchers globally. Here we used such an approach to characterize the evolutionary history of stiltgrass (Microstegium vimineum), one of the most damaging invasive grass species in North America. Previous examination of over 1,100 digitized herbarium records indicated that stiltgrass, first collected in Tennessee, USA in 1919 (specimen included here), spread rapidly throughout the southeastern USA. All specimens examined in the USA were awnless, until in the late 1930s an awned form appeared in the northeastern USA followed by subsequent regional spread, possibly revealing a second successful invasion. To test hypotheses of multiple invasions and spatiotemporal changes in population structure, we sequenced 139 contemporary and 126 historical stiltgrass samples from the native and invasive ranges (n = 121 for Asia and 144 for the USA, respectively). Mean coverage depth per sample of the 1.12 Gb genome was 4.76 ×, with a standard deviation of 2.94. Analysis of total population structure applying genotype likelihood methods and stringent filters, using all specimens, revealed two genetically distinct clusters of stiltgrass in the USA, corresponding to each hypothesized invasion, and further corresponding to two distinct awn phenotypes: predominantly awnless in the southeastern USA and awned in the northeastern USA, with evidence of admixture and a short-awned form at mid-latitudes. For example, “southern” genotypes are observed as far north as New York, while “northern” genotypes are observed as far south as Tennessee, including at the original site where stiltgrass was first collected over a century ago. Though sampling is not as comprehensive for earlier historical specimens from Asia relative to that in the US due to limited access to material, we observed a subset of the native-range variation in the invasive range overall, but a surprisingly high amount of diversity in the latter. Lastly, we quantified patterns of population structure in the invasive range across distinct time slices, documenting the spread of genotypes, subsequent secondary contact emanating from points of origin, admixture, and evidence of long-distance dispersal, likely due to anthropogenic causes. Our findings demonstrate the utility of studying widespread, established invaders for predicting patterns and invasion routes of more recently established species, such that we may be better equipped to predict and prevent potential problems caused by future invasions.