This paper reports a method for generating an intact and perfusable microvascular network that connects to microfluidic channels without appreciable leakage. This platform incorporates different stages of vascular development including vasculogenesis, endothelial cell (EC) lining, sprouting angiogenesis, and anastomosis in sequential order. After formation of a capillary network inside the tissue chamber via vasculogenesis, the adjacent microfluidic channels are lined with a monolayer of ECs, which then serve as the high-pressure input (“artery”) and low pressure output (“vein”) conduits. To promote a tight interconnection between the artery/vein and the capillary network, sprouting angiogenesis is induced, which promotes anastomosis of the vasculature inside the tissue chamber with the EC lining along the microfluidic channels. Flow of fluorescent microparticles confirms the perfusability of the lumenized microvascular network, and minimal leakage of 70 kDa FITC-dextran confirms physiologic tightness of the EC junctions and completeness of the interconnections between artery/vein and the capillary network. This versatile device design and its robust construction methodology establish a physiological transport model of interconnected perfused vessels from artery to vascularized tissue to vein. The system has utility in a wide range of organ-on-a-chip applications as it enables the physiological vascular interconnection of multiple on-chip tissue constructs that can serve as disease models for drug screening.