Swordfish (Xiphias gladius) is managed in the Atlantic Ocean and Mediterranean Sea as three major stocks, although their correspondence with underlying genomic population structure remains uncertain. Here, we combined a newly assembled reference genome with ddRAD sequencing of 575 swordfish from 14 Atlantic and Mediterranean areas to characterize genomic population structure and genetic differentiation relative to the current ICCAT management framework, evaluate individual stock assignment and ancestry across management boundaries, and compare genetic-diversity patterns among stocks and sampling areas. After quality control, 504 individuals were retained, with 26,324 SNPs used for diversity analyses and 15,049 LD-pruned SNPs for population-structure and assignment analyses. Multivariate analyses, pairwise differentiation, AMOVA, and ADMIXTURE consistently identified strong Mediterranean–Atlantic differentiation, whereas North and South Atlantic swordfish showed much weaker and partly continuous genomic structure. Formal stock identification, DAPC, and ADMIXTURE consistently assigned 11 individuals from Portugal and the Canary Islands to the Mediterranean stock. Within the Atlantic, ancestry patterns were more diffuse and included individuals with assignments discordant with their a priori management stock. Heterozygosity was broadly similar among stocks, whereas rarefied allelic richness was lower in the Mediterranean than in either Atlantic stock. Overall, the current management framework captures the major Mediterranean–Atlantic differentiation but only partially reflects the weaker genomic structure within the Atlantic. These findings show that population-genomic analyses can refine stock-structure inference and individual assignment while providing complementary information for swordfish assessment and monitoring.