Defining the ontogeny of the human adaptive immune system during embryogenesis has implications for understanding childhood diseases including leukaemias and autoimmune conditions. Using RAG1:GFP human pluripotent stem cell reporter lines, we examined human T-cell genesis from pluripotent-stem-cell-derived haematopoietic organoids. Under conditions favouring T-cell development, RAG1+ cells progressively upregulated a cohort of recognized T-cell-associated genes, arresting development at the CD4+CD8+ stage. Sort and re-culture experiments showed that early RAG1+ cells also possessed B-cell, myeloid and erythroid potential. Flow cytometry and single-cell-RNA-sequencing data showed that early RAG1+ cells co-expressed the endothelial/haematopoietic progenitor markers CD34, VECAD and CD90, whereas imaging studies identified RAG1+ cells within CD31+ endothelial structures that co-expressed SOX17+ or the endothelial marker CAV1. Collectively, these observations provide evidence for a wave of human T-cell development that originates directly from haemogenic endothelium via a RAG1+ intermediate with multilineage potential.