Structural variants (SVs) are a major source of genetic and phenotypic variation, but remain challenging to accurately type and are hence poorly characterized in most species. We present an approach for reliable SV discovery in non-model species using whole genome sequencing and report 15,483 high-confidence SVs in 492 Atlantic salmon (Salmo salar L.) sampled from a broad phylogeographic distribution. These SVs recover population genetic structure with high resolution, include an active DNA transposon, widely affect functional features, and overlap more duplicated genes retained from an ancestral salmonid autotetraploidization event than expected. Changes in SV allele frequency between wild and farmed fish indicate polygenic selection on behavioural traits during domestication, targeting brain-expressed synaptic networks linked to neurological disorders in humans. This study offers novel insights into the role of SVs in genome evolution and the genetic architecture of domestication traits, along with resources supporting reliable SV discovery in non-model species.