A major deficit in tissue engineering strategies is the lack of materials that promote angiogenesis, wherein endothelial cells from the host vasculature invade the implanted matrix to form new blood vessels. To determine the material properties that regulate angiogenesis, we have developed a microfluidic in vitro model in which chemokine-guided endothelial cell sprouting into a tunable hydrogel is followed by the formation of perfusable lumens. We show that long, perfusable tubes only develop if hydrogel adhesiveness and degradability are fine-tuned to support the initial collective invasion of endothelial cells and, at the same time, allow for matrix remodeling to permit the opening of lumens. These studies provide a better understanding of how cell-matrix interactions regulate angiogenesis and, therefore, constitute an important step towards optimal design criteria for tissue-engineered materials that require vascularization.