Control of cell polarity is crucial during tissue morphogenesis and renewal, and depends on spatial cues provided by the extracellular environment. Using micropatterned substrates to impose reproducible cell-cell interactions, we show that in the absence of other polarizing cues, cell-cell contacts are the main regulator of nucleus and centrosome positioning, and intracellular polarized organization. In a variety of cell types, including astrocytes, epithelial cells, and endothelial cells, calcium-dependent cadherin-mediated cell-cell interactions induce nucleus and centrosome off-centering toward cell-cell contacts, and promote orientation of the nucleus-centrosome axis toward free cell edges. Nucleus and centrosome off-centering is controlled by N-cadherin through the regulation of cell interactions with the extracellular matrix, whereas the orientation of the nucleus-centrosome axis is determined by the geometry of N-cadherin-mediated contacts. Our results demonstrate that in addition to the specific function of E-cadherin in regulating baso-apical epithelial polarity, classical cadherins control cell polarization in otherwise nonpolarized cells.