Mammalian cells respond to tactile cues from topographic elements presented by the substrate. Among these, anisotropic features distributed in an ordered manner give directionality. In the extracellular matrix, this ordering is embedded in a noisy environment altering the contact guidance effect. To date, it is unclear how cells respond to topographical signals in a noisy environment. Here, using rationally designed substrates, we report morphotaxis, a guidance mechanism enabling fibroblasts and epithelial cells to move along gradients of topographic order distortion. Isolated cells and cell ensembles perform morphotaxis in response to gradients of different strength and directionality, with mature epithelia integrating variations of topographic order over hundreds of micrometers. The level of topographic order controls cell cycle progression, locally delaying or promoting cell proliferation. In mature epithelia, the combination of morphotaxis and noise-dependent distributed proliferation provides a strategy to enhance wound healing as confirmed by a mathematical model capturing key elements of the process.