Human progenitor T cells that are able to successfully engraft a murine thymus and differentiate into mature human T and NK cells are described. The human progenitor T cells have the phenotype CD34+CD7+CD 1a−CD5− or CD34+CD7+CD1a−CD5+ and are derived from human hematopoietic stem cells, embryonic stem cells and induced pluripotent stem cells by coculture with cells expressing a Notch receptor ligand (OP9-DL1 or OP9-DL4). Such cells are useful in a variety of applications including immune reconstitution, the treatment of immunodeficiencies and as carriers for genes used in gene therapy.