Significant hybridization between the invasive North American fungal plant pathogen Heterobasidion irregulare and its Eurasian sister species H. annosum is ongoing in Italy. Whole genomes of nine natural hybrids were sequenced, assembled and compared with those of three genotypes each of the two parental species. Genetic relationships among hybrids and their level of admixture were determined. A multi-approach pipeline was used to assign introgressed genomic blocks to each of the two species. Alleles that introgressed from H. irregulare to H. annosum were associated with pathways putatively related to saprobic processes, while alleles that introgressed from the native to the invasive species were mainly linked to gene regulation. There was no overlap of allele categories introgressed in the two directions. Phenotypic experiments documented a fitness increase in H. annosum genotypes characterized by introgression of alleles from the invasive species, supporting the hypothesis that hybridization results in putatively adaptive introgression. Conversely, introgression from the native into the exotic species appeared to be driven by selection on genes favoring genome stability. Since the introgression of specific alleles from the exotic H. irregulare into the native H. annosum increased the invasiveness of the latter species, we propose that two invasions may be co-occurring: the first one by genotypes of the exotic species, and the second one by alleles belonging to the exotic species. Given that H. irregulare represents a threat to European forests, monitoring programs need to track not only exotic genotypes in native forest stands, but also exotic alleles introgressed in native genotypes.