The genomic variation of an invasive species may be affected by complex demographic histories and evolutionary changes during the invasion. Here, we describe the relative influence of bottlenecks, clonality, and population expansion in determining genomic variability of the widespread red macroalga Agarophyton vermiculophyllum. Its introduction from mainland Japan to the estuaries of North America and Europe coincided with shifts from predominantly sexual to partially clonal reproduction and rapid adaptive evolution. A survey of 62,285 SNPs for 351 individuals from 35 populations, aligned to 24 chromosome-length scaffolds indicate that linkage disequilibrium (LD), observed heterozygosity (Ho), Tajima's D, and nucleotide diversity (Pi) were greater among non-native than native populations. Evolutionary simulations indicate LD and Tajima's D were consistent with a severe population bottleneck. Also, the increased rate of clonal reproduction in the non-native range could not have produced the observed patterns by itself but may have magnified the bottleneck effect on LD. Elevated marker diversity in the genetic source populations could have contributed to the increased Ho and Pi observed in the non-native range. We refined the previous invasion source region to a ~50 km section of northeastern Honshu Island. Outlier detection methods failed to reveal any consistently differentiated loci shared among invaded regions, probably because of the complex A. vermiculophyllum demographic history. Our results reinforce the importance of demographic history, specifically founder effects, in driving genomic variation of invasive populations, even when localized adaptive evolution and reproductive system shifts are observed.