Blood-vessel formation generates unique vascular patterns in each individual. The principles governing the apparent stochasticity of this process remain to be elucidated. Using mathematical methods, we find that the transition between two fundamental vascular morphogenetic programs—sprouting angiogenesis and vascular remodeling—is established by a shift of collective front-to-rear polarity of endothelial cells in the mouse retina. We demonstrate that the competition between biochemical (VEGFA) and mechanical (blood-flow-induced shear stress) cues controls this collective polarity shift. Shear stress increases tension at focal adhesions overriding VEGFA-driven collective polarization, which relies on tension at adherens junctions. We propose that vascular morphogenetic cues compete to regulate individual cell polarity and migration through tension shifts that translates into tissue-level emergent behaviors, ultimately leading to uniquely organized vascular patterns.