Vascularization and efficient perfusion are long-standing challenges in cardiac tissue engineering. Here we report engineered perfusable microvascular constructs, wherein human embryonic stem cell-derived endothelial cells (hESC-ECs) are seeded both into patterned microchannels and the surrounding collagen matrix. In vitro, the hESC-ECs lining the luminal walls readily sprout and anastomose with de novo-formed endothelial tubes in the matrix under flow. When implanted on infarcted rat hearts, the perfusable microvessel grafts integrate with coronary vasculature to a greater degree than non-perfusable self-assembled constructs at 5 days post-implantation. Optical microangiography imaging reveal that perfusable grafts have 6-fold greater vascular density, 2.5-fold higher vascular velocities and >20-fold higher volumetric perfusion rates. Implantation of perfusable grafts containing additional hESC-derived cardiomyocytes show higher cardiomyocyte and vascular density. Thus, pre-patterned vascular networks enhance vascular remodeling and accelerate coronary perfusion, potentially supporting cardiac tissues after implantation. These findings should facilitate the next generation of cardiac tissue engineering design.