An arteriovenous shunt includes a self-expanding stent graft having a self-expanding anchor stent mounted eccentrically and externally about at least one end segment of the stent graft. A fluid passageway extends between open first and second ends of the shunt. The anchor stent has an expanded diameter greater than an expanded diameter of the stent graft. The expanded diameter of the stent graft is smaller than the artery or vein into which it is deployed. Methods of deploying the arteriovenous shunt are also disclosed.
