Tibetan sheep were introduced to the Qinghai Tibet plateau roughly 3,000 B.P., making this species a good model for investigating genetic mechanisms of high-altitude adaptation over a relatively short timescale. Here, we characterize genomic structural variants (SVs) that distinguish Tibetan sheep from closely related, low-altitude Hu sheep, and we examine associated changes in tissue-specific gene expression. We document differentiation between the two sheep breeds in frequencies of SVs associated with genes involved in cardiac function and circulation. In Tibetan sheep, we identified high-frequency SVs in a total of 462 genes, including
EPAS1
,
PAPSS2
, and
PTPRD
. Single-cell RNA-Seq data and luciferase reporter assays revealed that the SVs had
cis
-acting effects on the expression levels of these three genes in specific tissues and cell types. In Tibetan sheep, we identified a high-frequency chromosomal inversion that exhibited modified chromatin architectures relative to the noninverted allele that predominates in Hu sheep. The inversion harbors several genes with altered expression patterns related to heart protection, brown adipocyte proliferation, angiogenesis, and DNA repair. These findings indicate that SVs represent an important source of genetic variation in gene expression and may have contributed to high-altitude adaptation in Tibetan sheep.