Whole-genome duplication (WGD; or polyploidy) has played a major role in the evolution of many lineages however, our understanding of the processes that shape genome evolution following WGD remains incomplete. While polyploidy duplicates the entire genome sequence, it is rediploidisation that establishes inde- pendent duplicated genes. Rediploidisation proceeds through suppression of meiotic recombination across polysomic loci thus restoring disomic inheritance, a process that is not synchronised across the genome. Despite its importance, the mechanisms underlying this process remain poorly understood. The slowly evolving genomes of paleopolyploid Acipenseriformes paddlefish and sturgeon provide an invaluable system for investigating this, as rediploidisation was highly asynchronous in these lineages. In both genomes ohnologs tend to segregate into blocks on the chromo- somes according to rediploidisation timing, a pattern that suggests links between chromosomal structure and rediploidisation. Here, we analyse a newly-produced duplicate-resolved paddlefish genome assembly and show a strong concordance between genome rearrangement and rediploidisation timing. We also find that topologically associated domain (TAD) boundaries are associated with rediploidi- sation block boundaries. Together these results indicate that rediploidisation in acipenseriformes occurred through a process of genome rearrangements that was subject to functional constraints imposed by 3D genome architecture. We investigate the evolution of Hox clusters in these lineages, revealing a previously overlooked duplicate HoxC region in paddlefish, and both ancestral and lineage-specific Hox cluster rediploidisation with substantially different timings. These findings highlight a complex evolutionary history following WGD in Acipenseriformes with implica- tions for understanding short-term adaptations to polyploidy as well as longer-term diversification of lineages.