Chromosomal rearrangements, which shuffle DNA throughout the genome, are an important source of divergence across taxa. Using a paired-end read approach with Illumina sequence data for archaic humans, I identify changes in genome structure that occurred recently in human evolution. Hundreds of rearrangements indicate genomic trafficking between the sex chromosomes and autosomes, raising the possibility of sex-specific changes. Additionally, genes adjacent to genome structure changes in Neanderthals are associated with testis-specific expression, consistent with evolutionary theory that new genes commonly form with expression in the testes. I identify one case of new-gene creation through transposition from the Y chromosome to chromosome 10 that combines the 5′-end of the testis-specific geneFank1with previously untranscribed sequence. This new transcript experienced copy number expansion in archaic genomes, indicating rapid genomic change. Among rearrangements identified in Neanderthals, 13% are transposition of selfish genetic elements, whereas 32% appear to be ectopic exchange between repeats. In Denisovan, the pattern is similar but numbers are significantly higher with 18% of rearrangements reflecting transposition and 40% ectopic exchange between distantly related repeats. There is an excess of divergent rearrangements relative to polymorphism in Denisovan, which might result from nonuniform rates of mutation, possibly reflecting a burst of transposable element activity in the lineage that led to Denisovan. Finally, loci containing genome structure changes show diminished rates of introgression from Neanderthals into modern humans, consistent with the hypothesis that rearrangements serve as barriers to gene flow during hybridization. Together, these results suggest that this previously unidentified source of genomic variation has important biological consequences in human evolution.