Vascularization remains a critical challenge in tissue engineering. The development of vascular networks within densely populated and metabolically functional tissues facilitate transport of nutrients and removal of waste products, thus preserving cellular viability over a long period of time. Despite tremendous progress in fabricating complex tissue constructs in the past few years, approaches for controlled vascularization within hydrogel based engineered tissue constructs have remained limited. Here, we report a three dimensional (3D) micromolding technique utilizing bioprinted agarose template fibers to fabricate microchannel networks with various architectural features within photocrosslinkable hydrogel constructs. Using the proposed approach, we were able to successfully embed functional and perfusable microchannels inside methacrylated gelatin (GelMA), star poly(ethylene glycol-co-lactide) acrylate (SPELA), poly(ethylene glycol) dimethacrylate (PEGDMA) and poly(ethylene glycol) diacrylate (PEGDA) hydrogels at different concentrations. In particular, GelMA hydrogels were used as a model to demonstrate the functionality of the fabricated vascular networks in improving mass transport, cellular viability and differentiation within the cell-laden tissue constructs. In addition, successful formation of endothelial monolayers within the fabricated channels was confirmed. Overall, our proposed strategy represents an effective technique for vascularization of hydrogel constructs with useful applications in tissue engineering and organs on a chip.