Hematopoietic stem cell (HSC) transplantation is curative for malignant and genetic blood disorders, but is limited by donor availability and immune-mismatch. Deriving HSCs from patient-matched embryonic/induced-pluripotent stem cells (ESCs/iPSCs) could address these limitations. Prior efforts in murine models exploited ectopic HoxB4 expression to drive self-renewal and enable multi-lineage reconstitution, yet fell short in delivering robust lymphoid engraftment. Here, by titrating exposure of HoxB4-ESC-HSC to Notch ligands, we report derivation of engineered HSCs that self-renew, repopulate multi-lineage hematopoiesis in primary and secondary engrafted mice, and endow adaptive immunity in immune-deficient recipients. Single-cell analysis shows that following engraftment in the bone marrow niche, these engineered HSCs further specify to a hybrid cell type, in which distinct gene regulatory networks of hematopoietic stem/progenitors and differentiated hematopoietic lineages are co-expressed. Our work demonstrates engineering of fully functional HSCs via modulation of genetic programs that govern self-renewal and lineage priming.