The aberrant localization of proteins in cells is a key factor in the development of various diseases, including cancer and neurodegenerative disease. To better understand and potentially manipulate protein localization for therapeutic purposes, we engineered bifunctional compounds that bind to proteins in separate cellular compartments. We show these compounds induce nuclear import of cytosolic cargoes, using nuclear-localized BRD4 as a "carrier" for co-import and nuclear trapping of cytosolic proteins. We use this system to calculate kinetic constants for passive diffusion across the nuclear pore and demonstrate single-cell heterogeneity in response to these bifunctional molecules with cells requiring high carrier to cargo expression for complete import. We also observe incorporation of cargo into BRD4-containing condensates. Proteins shown to be substrates for nuclear transport include oncogenic mutant nucleophosmin (NPM1c) and mutant PI3K catalytic subunit alpha (PIK3CAE545K), suggesting potential applications to cancer treatment. In addition, we demonstrate that chemically induced localization of BRD4 to cytosolic-localized DNA-binding proteins, namely, IRF1 with a nuclear export signal, induces target gene expression. These results suggest that induced localization of proteins with bifunctional molecules enables the rewiring of cell circuitry, with significant implications for disease therapy.