Vascularizing printed tissues is a critical challenge in bioprinting. While protein-based hydrogel bioinks have been successfully used to bioprint microvasculature, their compositions are ill-defined and subject to batch variation. Few studies have focused on engineering proangiogenic bioinks with defined properties to direct endogenous microvascular network formation after printing. Here, a peptide-functionalized alginate hydrogel bioink with defined mechanical, rheological, and biochemical properties is developed for direct bioprinting of microvascularized tissues. An integrin-binding peptide (RGD) and a vascular endothelial growth factor-mimetic peptide with a protease-sensitive linker are conjugated onto a biodegradable alginate to synergistically promote vascular morphogenesis and capillary-scale endothelial tube formation. Partial ionic crosslinking before printing converts the otherwise unprintable hydrogel into a viscoelastic bioink with excellent printability and cytocompatibility. We use the bioink to fabricate a compartmentalized vascularized tissue construct, wherein we observe pericyte-endothelial cell colocalization and angiogenic sprouting across a tissue interface, accompanied by deposition of fibronectin and collagen in vascular and tissue components, respectively. This study provides a tunable and translational "off-the-shelf" hydrogel bioink with defined composition for vascularized bioprinting.