Chromosomal inversions are an important class of genetic variation that link multiple alleles together into a single inherited block that can have important effects on fitness. To study the role of large inversions in the massive evolutionary radiation of Lake Malawi cichlids, we used long-read technologies to identify four single and two tandem inversions that span half of each respective chromosome, and which together encompass over 10% of the genome. Each inversion is fixed in one of the two states within the seven major ecogroups, suggesting they played a role in the separation of the major lake lineages into specific lake habitats. One exception is within the benthic sub-radiation, where both inverted and non-inverted alleles continue to segregate within the group. The evolutionary histories of three of the six inversions suggest they transferred from the pelagic Diplotaxodon group into benthic ancestors at the time the benthic sub-radiation was seeded. The remaining three inversions are found in a subset of benthic species living in deep waters. We show that some of these inversions are used as XY sex-determination systems but are also likely limited to a subset of total lake species. Our work suggests that inversions have been under both sexual and natural selection in Lake Malawi cichlids and that they will be important to understanding how this adaptive radiation evolved.