The lack of sufficient numbers of donor organs for human transplantation therapies results in the loss of tens of thousands of lives and costs hundreds of billions of dollars each year in the US alone. However, the ability to create, de novo, functional organ replacements for treating human pathologies is fundamentally limited by the lack of a comprehensive vascularization strategy for engineered three-dimensional (3D) tissues. To understand the means by which the cellular microenvironment impinges on angiogenesis – the sprouting of new blood vessels from pre-existing ones – we developed a new family of synthetic and degradable hydrogels to tease apart interactions between endothelial cells and the extracellular matrix (ECM) during 3D angiogenic sprouting. We show that endothelial cell sprouting requires specific adhesive and degradable characteristics of the ECM over a narrow stiffness regime. At the mesoscale, we developed 3D printing materials and sacrificial casting strategies to enable the rapid fabrication of engineered tissues containing perfusable vascular architectures. Patterned vasculature facilitated capillary sprouting and supported the function of primary hepatocytes in centimeter-sized constructs. Together these technologies provide a flexible platform for a wide array of specific applications, and may enable the scaling of densely populated tissue constructs to arbitrary size.