In vitro fabrication of functional vascularized three-dimensional tissues has been a long-standing objective in the field of tissue engineering. Here we report a technique to engineer cardiac tissues with perfusable blood vessels in vitro. Using resected tissue with a connectable artery and vein as a vascular bed, we overlay triple-layer cardiac cell sheets produced from coculture with endothelial cells, and support the tissue construct with media perfused in a bioreactor. We show that endothelial cells connect to capillaries in the vascular bed and form tubular lumens, creating in vitro perfusable blood vessels in the cardiac cell sheets. Thicker engineered tissues can be produced in vitro by overlaying additional triple-layer cell sheets. The vascularized cardiac tissues beat and can be transplanted with blood vessel anastomoses. This technique may create new opportunities for in vitro tissue engineering and has potential therapeutic applications.