White blood cells (leukocytes) come form pluripotent hematopoetic stem cells. Stem cells in the bone marrow differentiate into white blood cells.
However there are many types of white blood cells and although they all start development in the bone marrow, not all of them complete their development there. The types of different leukocytes are:
All of these cells start in the bone marrow as pluripotent hematopoetic stem cells. They then divide to form specialized stem cells and either become a myeloid progenitor or a lymphoid progenitor. These cells receive various signals and growth factors to enable them to divide into the wide variety of leukocytes named above.