Parasexuality contributes to diversity and adaptive evolution of haploid (monokaryotic) fungi. However, non-sexual genetic exchange mechanisms are not defined in dikaryotic fungi (containing two distinct haploid nuclei). Newly emerged strains of the wheat stem rust pathogen, Puccinia graminis f. sp. tritici (Pgt), such as Ug99, are a major threat to global food security. Here, we provide genomics-based evidence supporting that Ug99 arose by somatic hybridisation and nuclear exchange between dikaryons. Fully haplotype-resolved genome assembly and DNA proximity analysis reveal that Ug99 shares one haploid nucleus genotype with a much older African lineage of Pgt, with no recombination or chromosome reassortment. These findings indicate that nuclear exchange between dikaryotes can generate genetic diversity and facilitate the emergence of new lineages in asexual fungal populations.