Zinc-finger recombinases (ZFRs) represent a potentially powerful class of tools for targeted genetic engineering. These chimeric enzymes are composed of an activated catalytic domain derived from the resolvase/invertase family of serine recombinases and a custom-designed zinc-finger DNA-binding domain. The use of ZFRs, however, has been restricted by sequence requirements imposed by the recombinase catalytic domain. Here, we combine substrate specificity analysis and directed evolution to develop a diverse collection of Gin recombinase catalytic domains capable of recognizing an estimated 3.77 × 107 unique DNA sequences. We show that ZFRs assembled from these engineered catalytic domains recombine user-defined DNA targets with high specificity, and that designed ZFRs integrate DNA into targeted endogenous loci in human cells. This study demonstrates the feasibility of generating customized ZFRs and the potential of ZFR technology for a diverse range of applications, including genome engineering, synthetic biology and gene therapy.