The in vivo efficacy of engineered tissue constructs depends largely on their integration with the host vasculature. Prevascularisation has been noted to facilitate integration of the constructs via anastomosis of preformed microvascular networks. Here we report a technique to fabricate aligned, spatially defined prevascularised tissue constructs with endothelial vessels by assembling individually tailored cell-laden polyelectrolyte hydrogel fibres. Stable, aligned endothelial vessels form in vitro within these constructs in 24 h, and these vessels anastomose with the host circulation in a mouse subcutaneous model. We create vascularised adipose and hepatic tissues by co-patterning the respective cell types with the preformed endothelial vessels. Our study indicates that the formation of aligned endothelial vessels in a hydrogel is an efficient prevascularisation approach in the engineering of tissue constructs.