Methods for homologously recombining an exogenous nucleic acid into a target cell genome of a target cell are provided. In the subject methods, a targeting vector that includes a linearizing endonuclease site, e.g., a recombinase recognition site, and a homologous recombination integrating element, is contacted with the target cell(s) such that the target cell(s) take up the targeting vector. The targeting vector is originally a circular targeting vector that is linearized by a linearizing endonuclease, e.g., a recombinase, either prior to administration (e.g., in vitro treatment with an endonuclease) or upon entry into the multicellular organism by endonucleases in the extracellular or intracellular fluids that can be introduced to or already present in the muticellular organism. The integrating element homologously recombines into the target cell genome from the linearized targeting vector. Also provided are targeting vectors, systems and kits for use in practicing the subject methods.