Neoantigens unique to each patient's tumor can be recognized by autologous T cells through their T-cell receptor (TCR) but the low frequency and/or terminal differentiation of mutation-specific T cells in tumors can limit their utility as adoptive T-cell therapies. Transfer of TCR genes into younger T cells from peripheral blood with a high proliferative potential could obviate this problem. We generated a rapid, cost-effective strategy to genetically engineer cancer patient T cells with TCRs using the clinical Sleeping Beauty transposon/transposase system. Patient-specific TCRs reactive against HLA-A*0201-restriced neoantigens AHNAK^S2580F or ERBB2^H473Y or the HLA-DQB*0601-restricted neoantigen ERBB2IP^E805G were assembled with murine constant chains and cloned into Sleeping Beauty transposons. Patient peripheral blood lymphocytes were coelectroporated with SB11 transposase and Sleeping Beauty transposon, and transposed T cells were enriched by sorting on murine TCRβ (mTCRβ) expression. Rapid expansion of mTCRβ⁺ T cells with irradiated allogeneic peripheral blood lymphocytes feeders, OKT3, interleukin-2 (IL-2), IL-15, and IL-21 resulted in a preponderance of effector (CD27⁻CD45RA⁻) and less-differentiated (CD27⁺CD45RA⁺) T cells. Transposed T cells specifically mounted a polyfunctional response against cognate mutated neoantigens and tumor cell lines. Thus, Sleeping Beauty transposition of mutation-specific TCRs can facilitate the use of personalized T-cell therapy targeting unique neoantigens.