Genomic parasites have evolved distinctive lifestyles to optimize replication in the context of the genomes they inhabit. Here, we introduced new DNA into eukaryotic cells using bacteriophage Mu DNA transposition complexes, termed ‘transpososomes’. Following electroporation of transpososomes and selection for marker gene expression, efficient integration was verified in yeast, mouse and human genomes. Although Mu has evolved in prokaryotes, strong biases were seen in the target site distributions in eukaryotic genomes, and these biases differed between yeast and mammals. In Saccharomyces cerevisiae transposons accumulated outside of genes, consistent with selection against gene disruption. In mouse and human cells, transposons accumulated within genes, which previous work suggests is a favorable location for efficient expression of selectable markers. Naturally occurring transposons and viruses in yeast and mammals show related, but more extreme, targeting biases, suggesting that they are responding to the same pressures. These data help clarify the constraints exerted by genome structure on genomic parasites, and illustrate the wide utility of the Mu transpososome technology for gene transfer in eukaryotic cells.