3D bioprinting is an emerging additive manufacturing technique to fabricate constructs for human disease modeling. However, current cell‐laden bioinks lack sufficient biocompatibility, printability, and structural stability needed to translate this technology to preclinical and clinical trials. Here, a new class of nanoengineered hydrogel‐based cell‐laden bioinks is introduced, that can be printed into 3D, anatomically accurate, multicellular blood vessels to recapitulate both the physical and chemical microenvironments of native human vasculature. A remarkably unique characteristic of this bioink is that regardless of cell density, it demonstrates a high printability and ability to protect encapsulated cells against high shear forces in the bioprinting process. 3D bioprinted cells maintain a healthy phenotype and remain viable for nearly one‐month post‐fabrication. Leveraging these properties, the nanoengineered bioink is printed into 3D cylindrical blood vessels, consisting of living co‐culture of endothelial cells and vascular smooth muscle cells, providing the opportunity to model vascular function and pathophysiology. Upon cytokine stimulation and blood perfusion, this 3D bioprinted vessel is able to recapitulate thromboinflammatory responses observed only in advanced in vitro preclinical models or in vivo. Therefore, this 3D bioprinted vessel provides a potential tool to understand vascular disease pathophysiology and assess therapeutics, toxins, or other chemicals.