Signaling by Nodal and Bmp is essential for cardiac laterality. How activities of these pathways translate into left-right asymmetric organ morphogenesis is largely unknown. We show that, in zebrafish, Nodal locally reduces Bmp activity on the left side of the cardiac field. This effect is mediated by the extracellular matrix enzyme Hyaluronan synthase 2, expression of which is induced by Nodal. Unilateral reduction of Bmp signaling results in lower expression of nonmuscle myosin II and higher cell motility on the left, driving asymmetric displacement of the entire cardiac field. In silico modeling shows that left-right differences in cell motility are sufficient to induce a robust, directional migration of cardiac tissue. Thus, the mechanism underlying the formation of cardiac left-right asymmetry involves Nodal modulating an antimotogenic Bmp activity.