Mammalian synthetic biology may provide novel therapeutic strategies, help decipher new paths for drug discovery and facilitate synthesis of valuable molecules. Yet, our capacity to genetically program cells is currently hampered by the lack of efficient approaches to streamline the design, construction and screening of synthetic gene networks. To address this problem, here we present a framework for modular and combinatorial assembly of functional (multi)gene expression vectors and their efficient and specific targeted integration into a well-defined chromosomal context in mammalian cells. We demonstrate the potential of this framework by assembling and integrating different functional mammalian regulatory networks including the largest gene circuit built and chromosomally integrated to date (6 transcription units, 27kb) encoding an inducible memory device. Using a library of 18 different circuits as a proof of concept, we also demonstrate that our method enables one-pot/single-flask chromosomal integration and screening of circuit libraries. This rapid and powerful prototyping platform is well suited for comparative studies of genetic regulatory elements, genes and multi-gene circuits as well as facile development of libraries of isogenic engineered cell lines.