The Sleeping Beauty (SB) transposon system is an efficient non-viral gene transfer tool in mammalian cells, but its broad use has been hampered by uncontrolled transposase gene activity from DNA vectors, posing a risk of genome instability, and by the inability to use the transposase protein directly. In this study, we used rational protein design based on the crystal structure of the hyperactive SB100X variant to create an SB transposase (high-solubility SB, hsSB) with enhanced solubility and stability. We demonstrate that hsSB can be delivered with transposon DNA to genetically modify cell lines and embryonic, hematopoietic and induced pluripotent stem cells (iPSCs), overcoming uncontrolled transposase activity. We used hsSB to generate chimeric antigen receptor (CAR) T cells, which exhibit potent antitumor activity in vitro and in xenograft mice. We found that hsSB spontaneously penetrates cells, enabling modification of iPSCs and generation of CAR T cells without the use of transfection reagents. Titration of hsSB to modulate genomic integration frequency achieved as few as two integrations per genome.