Salmonids have a remarkable ability to form sympatric morphs after postglacial colonization of freshwater lakes. These morphs often differ in morphology, feeding, and spawning behaviour. Here, we explored the genetics of morph differentiation by establishing a high-quality, annotated reference genome for the Arctic charr and using this for population genomic analysis of morphs from two Norwegian and two Icelandic lakes. The four lakes represent the spectrum of genetic differentiation between morphs from one lake with no genetic differentiation between morphs, implying phenotypic plasticity, to two lakes with locus-specific genetic differentiation, implying incomplete reproductive isolation, and one lake with strong genome-wide divergence consistent with complete reproductive isolation. As many as 12 putative inversions ranging from 0.45 to 3.25 Mbp in size segregated among the four morphs present in one lake, Thingvallavatn, and these contributed significantly to the genetic differentiation among morphs. None of the putative inversions was found in any of the other lakes, but there were cases of partial haplotype sharing in similar morph contrasts in other lakes. The results are consistent with a highly polygenic basis of morph differentiation with limited genetic parallelism between lakes. The results support a model where morph differentiation is first established through phenotypic plasticity, leading to niche expansion and separation. This is followed by gradual development of reproductive isolation, locus-specific differentiation, and eventually complete reproductive isolation and genome-wide divergence. A major explanation for salmonids' ability to diversify into multiple sympatric morphs is likely their genome complexity from ancient whole genome duplication, which enhances evolvability.