Background: The circum-basmati group of cultivated Asian rice (Oryza sativa) contains many iconic varieties and is widespread in the Indian subcontinent. Despite its economic and cultural importance, a high-quality reference genome is currently lacking, and the group's evolutionary history is not fully resolved. To address these gaps, we use long-read nanopore sequencing and assemble the genomes of two circum-basmati rice varieties. Results: We generate two high-quality, chromosome-level reference genomes that represent the 12 chromosomes of Oryza. The assemblies show a contig N50 of 6.32 Mb and 10.53 Mb for Basmati 334 and Dom Sufid, respectively. Using our highly contiguous assemblies, we characterize structural variations segregating across circum-basmati genomes. We discover repeat expansions not observed in japonica-the rice group most closely related to circumbasmati-as well as the presence and absence variants of over 20 Mb, one of which is a circum-basmati-specific deletion of a gene regulating awn length. We further detect strong evidence of admixture between the circumbasmati and circum-aus groups. This gene flow has its greatest effect on chromosome 10, causing both structural variation and single-nucleotide polymorphism to deviate from genome-wide history. Lastly, population genomic analysis of 78 circum-basmati varieties shows three major geographically structured genetic groups: Bhutan/Nepal, India/Bangladesh/Myanmar, and Iran/Pakistan. Conclusion: The availability of high-quality reference genomes allows functional and evolutionary genomic analyses providing genome-wide evidence for gene flow between circum-aus and circum-basmati, describes the nature of circum-basmati structural variation, and reveals the presence/absence variation in this important and iconic rice variety group.