A cell therapy strategy utilizing genetically-corrected induced pluripotent stem cells (iPSC) may be an attractive approach for genetic disorders such as muscular dystrophies. Methods for genetic engineering of iPSC that emphasize precision and minimize random integration would be beneficial. We demonstrate here an approach in the mdx mouse model of Duchenne muscular dystrophy that focuses on the use of site-specific recombinases to achieve genetic engineering. We employed non-viral, plasmid-mediated methods to reprogram mdx fibroblasts, using phiC31 integrase to insert a single copy of the reprogramming genes at a safe location in the genome. We next used Bxb1 integrase to add the therapeutic full-length dystrophin cDNA to the iPSC in a site-specific manner. Unwanted DNA sequences, including the reprogramming genes, were then precisely deleted with Cre resolvase. Pluripotency of the iPSC was analyzed before and after gene addition, and ability of the genetically corrected iPSC to differentiate into myogenic precursors was evaluated by morphology, immunohistochemistry, qRT-PCR, FACS analysis, and intramuscular engraftment. These data demonstrate a non-viral, reprogramming-plus-gene addition genetic engineering strategy utilizing site-specific recombinases that can be applied easily to mouse cells. This work introduces a significant level of precision in the genetic engineering of iPSC that can be built upon in future studies.