Abstract The genetic paradox of biological invasions is complex and multifaceted. In particular, the relative role of disparate propagule sources and genetic adaptation through postintroduction hybridization has remained largely unexplored. To add resolution to this paradox, we investigate the genetic architecture responsible for the invasion of two invasive Asian carp species, bighead carp (Hypophthalmichthys nobilis) and silver carp (H. molitrix) (bigheaded carps) that experience extensive hybridization in the Mississippi River Basin (MRB). We sequenced the genomes of bighead and silver carps (~1.08G bp and ~1.15G bp, respectively) and their hybrids collected from the MRB. We found moderate‐to‐high heterozygosity in bighead (0.0021) and silver (0.0036) carps, detected significantly higher dN/dS ratios of single‐copy orthologous genes in bigheaded carps versus 10 other species of fish, and identified genes in both species potentially associated with environmental adaptation and other invasion‐related traits. Additionally, we observed a high genomic similarity (96.3% in all syntenic blocks) between bighead and silver carps and over 90% embryonic viability in their experimentally induced hybrids. Our results suggest intrinsic genomic features of bigheaded carps, likely associated with life history traits that presumably evolved within their native ranges, might have facilitated their initial establishment of invasion, whereas ex-situ interspecific hybridization between the carps might have promoted their range expansion. This study reveals an alternative mechanism that could resolve one of the genetic paradoxes in biological invasions and provides invaluable genomic resources for applied research involving bigheaded carps.