The bioengineering of artificial tissue constructs requires special attention to their fast vascularization to provide cells with sufficient nutrients and oxygen. We addressed the challenge of in vitro vascularization by employing a combined approach of cell sheet engineering, 3D printing, and cellular self-organization in dynamic maturation culture. A confluent cell sheet of human umbilical vein endothelial cells (HUVECs) was detached from a thermoresponsive cell culture substrate and transferred onto a 3D-printed, perfusable tubular scaffold using a custom-made cell sheet rolling device. Under indirect co-culture conditions with human dermal fibroblasts (HDFs), the cell sheet-covered vessel mimic embedded in a collagen gel together with additional singularized HUVECs started sprouting into the surrounding gel, while the suspended cells around the tube self-organized and formed a dense lumen-containing 3D vascular network throughout the gel. The HDFs cultured below the HUVEC-containing cell culture insert provided angiogenic support to the HUVECs via molecular crosstalk without competing for space with the HUVECs or inducing rapid collagen matrix remodeling. The resulting vascular network remained viable under these conditions throughout the 3 week cell culture period. This static indirect co-culture setup was further transferred to dynamic flow conditions, where the medium perfusion was enabled via two independently addressable perfusion circuits equipped with two different cell culture chambers, one hosting the HDFs and the other hosting the HUVEC-laden collagen gel. Using this system, we successfully connected the collagen-embedded HUVEC culture to a dynamic medium flow, and within 1 week of the dynamic cell culture, we detected angiogenic sprouting and dense microvascular network formation via HUVEC self-organization in the hydrogel. Our approach of combining a 3D-printed and cell sheet-covered vascular precursor that retained its sprouting capacity together with the self-assembling HUVECs in a dynamic perfusion culture resulted in a vascular-like 3D network, which is a critical step toward the long-term vascularization of bioengineered in vitro tissue constructs.