In adaptive radiations, single lineages rapidly diversify by adapting to many new niches. Little is known yet about the genomic mechanisms involved, that is, the source of genetic variation or genomic architecture facilitating or constraining adaptive radiation. Here, we investigate genomic changes associated with repeated invasion of many different freshwater niches by threespine stickleback in the Haida Gwaii archipelago, Canada, by resequencing single genomes from one marine and 28 freshwater populations. We find 89 likely targets of parallel selection in the genome that are enriched for old standing genetic variation. In contrast to theoretical expectations, their genomic architecture is highly dispersed with little clustering. Candidate genes and genotype-environment correlations match the three major environmental axes predation regime, light environment, and ecosystem size. In a niche space with these three dimensions, we find that the more divergent a new niche from the ancestral marine habitat, the more loci show signatures of parallel selection. Our findings suggest that the genomic architecture of parallel adaptation in adaptive radiation depends on the steepness of ecological gradients and the dimensionality of the niche space.