The development of vascular networks in microfluidic chips is crucial for the long-term culture of three-dimensional cell aggregates such as spheroids, organoids, tumoroids, or tissue explants. Despite rapid advancement in microvascular network systems and organoid technologies, vascularizing organoids-on-chips remains a challenge in tissue engineering. Most existing microfluidic devices poorly reflect the complexity of in vivo flows and require complex technical set-ups. Considering these constraints, we develop a platform to establish and monitor the formation of endothelial networks around mesenchymal and pancreatic islet spheroids, as well as blood vessel organoids generated from pluripotent stem cells, cultured for up to 30 days on-chip. We show that these networks establish functional connections with the endothelium-rich spheroids and vascular organoids, as they successfully provide intravascular perfusion to these structures. We find that organoid growth, maturation, and function are enhanced when cultured on-chip using our vascularization method. This microphysiological system represents a viable organ-on-chip model to vascularize diverse biological 3D tissues and sets the stage to establish organoid perfusions using advanced microfluidics.