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The spread of staple crops to diverse environments over time and their current genetic structure may reflect historical dispersal by humans, sustained human preference for particular traits and adaptation to local environments. Sorghum is a drought-tolerant crop native to Africa cultivated by hundreds of millions of smallholders globally. Here we examined the ecological context of population-genomic structure of 1806 sorghum landraces across Africa and Eurasia to infer the relative contribution of environmental and cultural factors to sorghum genetic diversity across different relative time periods. Sorghum landraces were spatially and linguistically structured at a large scale and within subregions, following a pattern of isolation by distance. Within regions, much of the genomic structure was best explained by a mechanistic model of human travel time. In our assessment of hierarchical linguistic structure, we found that language families explain 4% of genomic variation while individual languages explain 13% of genomic variation, suggesting the importance of human culture and relationships in gene flow and selection. Variance partitioning showed that travel time, language and climate explain up to 27% of genomic variation among landraces. We also observed regional differences in the degree of genetic relatedness across space and time in our assessment of shared ancestry. East Africa showed particularly strong geographic turnover in genomic composition and haplotype sharing, while West Africa showed substantial haplotype sharing even over large distances, signifying some rapidly spreading lineages. Thus, space, travel time and culture likely capture important forces controlling sorghum genomic variation, but these factors operate heterogeneously over space.