Engineering cells for adoptive therapy requires overcoming limitations in cell viability and, in the efficiency of transgene delivery, the duration of transgene expression and the stability of genomic integration. Here we report a gene-delivery system consisting of a Sleeping Beauty (SB) transposase encoded into a messenger RNA delivered by an adeno-associated virus (AAV) encoding an SB transposon that includes the desired transgene, for mediating the permanent integration of the transgene. Compared with lentiviral vectors and with the electroporation of plasmids of transposon DNA or minicircle DNA, the gene-delivery system, which we named MAJESTIC (for 'mRNA AAV-SB joint engineering of stable therapeutic immune cells'), offers prolonged transgene expression, as well as higher transgene expression, therapeutic-cell yield and cell viability. MAJESTIC can deliver chimeric antigen receptors (CARs) into T cells (which we show lead to strong anti-tumour activity in vivo) and also transduce natural killer cells, myeloid cells and induced pluripotent stem cells with bi-specific CARs, kill-switch CARs and synthetic T-cell receptors.