A variety of tissue lineages can be differentiated from pluripotent stem cells by mimicking embryonic development through stepwise exposure to morphogens, or by conversion of one differentiated cell type into another by enforced expression of master transcription factors. Here, to yield functional human haematopoietic stem cells, we perform morphogen-directed differentiation of human pluripotent stem cells into haemogenic endothelium followed by screening of 26 candidate haematopoietic stem-cell-specifying transcription factors for their capacity to promote multi-lineage haematopoietic engraftment in mouse hosts. We recover seven transcription factors (ERG, HOXA5, HOXA9, HOXA10, LCOR, RUNX1 and SPI1) that are sufficient to convert haemogenic endothelium into haematopoietic stem and progenitor cells that engraft myeloid, B and T cells in primary and secondary mouse recipients. Our combined approach of morphogen-driven differentiation and transcription-factor-mediated cell fate conversion produces haematopoietic stem and progenitor cells from pluripotent stem cells and holds promise for modelling haematopoietic disease in humanized mice and for therapeutic strategies in genetic blood disorders.