Symmetry-breaking polarization enables functional plasticity of cells and tissues and is yet not well understood. Here we show that epithelial cells, hard-wired to maintain a static morphology and to preserve tissue organization, can spontaneously switch to a migratory polarized phenotype after relaxation of the actomyosin cytoskeleton. We find that myosin II engages actin in the formation of cortical actomyosin bundles and thus makes it unavailable for deployment in the process of dendritic growth normally driving cell motility. Under low-contractility regimes, epithelial cells polarize in a front-back manner owing to the emergence of actin retrograde flows powered by dendritic polymerization of actin. Coupled to cell movement, the flows transport myosin II from the front to the back of the cell, where the motor locally 'locks' actin in contractile bundles. This polarization mechanism could be employed by embryonic and cancer epithelial cells in microenvironments where high-contractility-driven cell motion is inefficient.