Supergenes link allelic combinations into non-recombining units known to play an essential role in maintaining adaptive genetic variation. However, because supergenes can be maintained over millions of years by balancing selection and typically exhibit strong recombination suppression, both the underlying functional variants and how the supergenes are formed are largely unknown. Particularly, questions remain over the importance of inversion breakpoint sequences and whether supergenes capture pre-existing adaptive variation or accumulate this following recombination suppression. To investigate the process of supergene formation, we identified inversion polymorphisms in Atlantic salmon by assembling eleven genomes with nanopore long-read sequencing technology. A genome assembly from the sister species, brown trout, was used to determine the standard state of the inversions. We found evidence for adaptive variation through genotype–environment associations, but not for the accumulation of deleterious mutations. One young 3 Mb inversion segregating in North American populations has captured adaptive variation that is still segregating within the standard arrangement of the inversion, while some adaptive variation has accumulated after the inversion. This inversion and two others had breakpoints disrupting genes. Three multigene inversions with matched repeat structures at the breakpoints did not show any supergene signatures, suggesting that shared breakpoint repeats may obstruct supergene formation. This article is part of the theme issue ‘Genomic architecture of supergenes: causes and evolutionary consequences’.