Arterial bypass grafts remain the gold standard for the treatment of end-stage ischaemic disease. Yet patients unable to tolerate the cardiovascular stress of arterial surgery or those with unreconstructable disease would benefit from grafts that are able to induce therapeutic angiogenesis. Here, we introduce an approach whereby implantation of 3D-printed grafts containing endothelial-cell-lined lumens induces spontaneous, geometrically guided generation of collateral circulation in ischaemic settings. In rodent models of hind-limb ischaemia and myocardial infarction, we demonstrate that the vascular patches rescue perfusion of distal tissues, preventing capillary loss, muscle atrophy and loss of function. Inhibiting anastomoses between the construct and the host's local capillary beds, or implanting constructs with unpatterned endothelial cells, abrogates reperfusion. Our 3D-printed grafts constitute an efficient and scalable approach to engineer vascular patches able to guide rapid therapeutic angiogenesis and perfusion for the treatment of ischaemic diseases.