Despite recent advances in genome engineering made possible by the emergence of site-specific endonucleases, there remains a need for tools capable of specifically delivering genetic payloads into the human genome. Hybrid recombinases based on activated catalytic domains derived from the resolvase/invertase family of serine recombinases fused to Cys2-His2 zinc-finger or TAL effector DNA-binding domains are a class of reagents capable of achieving this. The utility of these enzymes, however, has been constrained by their low overall targeting specificity, largely due to the formation of side-product homodimers capable of inducing off-target modifications. Here, we combine rational design and directed evolution to re-engineer the serine recombinase dimerization interface and generate a recombinase architecture that reduces formation of these undesirable homodimers by >500-fold. We show that these enhanced recombinases demonstrate substantially improved targeting specificity in mammalian cells and achieve rates of site-specific integration similar to those previously reported for site-specific nucleases. Additionally, we show that enhanced recombinases exhibit low toxicity and promote the delivery of the human coagulation factor IX and α-galactosidase genes into endogenous genomic loci with high specificity. These results provide a general means for improving hybrid recombinase specificity by protein engineering and illustrate the potential of these enzymes for basic research and therapeutic applications.