Demographic modeling is often used with population genomic data to infer the relationships and ages among populations. However, relatively few analyses are able to validate these inferences with independent data. Here, we leverage written records that describe distinct Brassica rapa crops to corroborate demographic models of domestication. Brassica rapa crops are renowned for their outstanding morphological diversity, but the relationships and order of domestication remains unclear. We generated genome-wide SNPs from 126 accessions collected globally using high-throughput transcriptome data. Analyses of more than 31,000 SNPs across the B. rapa genome revealed evidence for five distinct genetic groups and supported a European-Central Asian origin of B. rapa crops. Our results supported the traditionally recognized South Asian and East Asian B. rapa groups with evidence that pak choi, Chinese cabbage, and yellow sarson are likely monophyletic groups. In contrast, the oil-type B. rapa subsp. oleifera and brown sarson were polyphyletic. We also found no evidence to support the contention that rapini is the wild type or the earliest domesticated subspecies of B. rapa. Demographic analyses suggested that B. rapa was introduced to Asia 2400-4100 years ago, and that Chinese cabbage originated 1200-2100 years ago via admixture of pak choi and European-Central Asian B. rapa. We also inferred significantly different levels of founder effect among the B. rapa subspecies. Written records from antiquity that document these crops are consistent with these inferences. The concordance between our age estimates of domestication events with historical records provides unique support for our demographic inferences.