Although there are various pre‐existing technologies for engineering vasculatures, multiscale modeling of the architecture of human vasculature at a capillary scale remains a challenge. In this study, a novel technology is developed for the production of a functional, multiscale microvasculature comprising of endothelialized channels and tissue‐specific capillary networks. Perfusable, endothelialized channels are bioprinted, after which angiogenic sprouts are grown into user‐designed capillary networks. The induction of branched and liver‐lobule‐like capillary networks confirm that the technology can produce various types of tissue‐specific multiscale microvasculatures. Further, the channels and capillaries are deemed to be functional when evaluated in vitro. An ex vivo assay demonstrates that the microvasculature can induce neovessel ingrowth, integrate with host vessels, and facilitate blood flow. Remarkably, blood flows through the implanted capillary network without any change in its morphology. Finally, the technology is applied to produce a vascularized liver tissue; it significantly improves its hepatic function. It is believed that this new technology will create new possibilities in the development of highly vascularized and functional tissues/organs on a clinically relevant scale.