Post-fabrication formation of a proper vasculature remains an unresolved challenge in bioprinting. Established strategies focus on the supply of the fabricated structure with nutrients and oxygen and either rely on the mere formation of a channel system using fugitive inks, or additionally use mature endothelial cells and/or peri-endothelial cells such as smooth muscle cells for the formation of blood vessels in vitro. Functional vessels, however, exhibit a hierarchical organization and multilayered wall structure that is important for their function. Human induced pluripotent stem cell-derived mesodermal progenitor cells (hiMPCs) have been shown to possess the capacity to form blood vessels in vitro, but have so far not been assessed for their applicability in bioprinting processes. Here, we demonstrate that hiMPCs, after formulation into an alginate/collagen type 1 bioink and subsequent extrusion, retain their ability to give rise to the formation of complex vessels that display a hierarchical network in a process that mimicks the embryonic steps of vessel formation by vasculogenesis. Histological evaluations at different time points of extrusion revealed initial formation of spheres, followed by lumen formation and further structural maturation as evidenced by building a multilayered vessel wall and a vascular network. These findings are supported by immunostainings for endothelial and peri-endothelial cell markers as well as electron microscopic analyses at the ultrastructural level. Moreover, capillary-like vessel structures deposited a basement membrane-like matrix structure at the basal side between the vessel wall and the alginate-collagen matrix. These results evidence the applicability and great potential of hiMPCs for the bioprinting of vascular structures mimicking the basic morphogenetic steps of de novo vessel formation during embryogenesis.