The wild relatives and progenitors of wheat have been widely used as sources of disease resistance (R) genes. Molecular identification and characterization of these R genes facilitates their manipulation and tracking in breeding programmes. Here, we develop a reference-quality genome assembly of the wild diploid wheat relative Aegilops sharonensis and use positional mapping, mutagenesis, RNA-Seq and transgenesis to identify the stem rust resistance gene Sr62, which has also been transferred to common wheat. This gene encodes a tandem kinase, homologues of which exist across multiple taxa in the plant kingdom. Stable Sr62 transgenic wheat lines show high levels of resistance against diverse isolates of the stem rust pathogen, highlighting the utility of Sr62 for deployment as part of a polygenic stack to maximize the durability of stem rust resistance.