Living cells and the extracellular matrix (ECM) can exhibit complex interactions that define key developmental, physiological and pathological processes. Here, we report a new type of directed migration—which we term ‘topotaxis’—guided by the gradient of the nanoscale topographic features in the cells’ ECM environment. We show that the direction of topotaxis is reflective of the effective cell stiffness, and that it depends on the balance of the ECM-triggered signalling pathways PI(3)K–Akt and ROCK–MLCK. In melanoma cancer cells, this balance can be altered by different ECM inputs, pharmacological perturbations or genetic alterations, particularly a loss of PTEN in aggressive melanoma cells. We conclude that topotaxis is a product of the material properties of cells and the surrounding ECM, and propose that the invasive capacity of many cancers may depend broadly on topotactic responses, providing a potentially attractive mechanism for controlling invasive and metastatic behaviour.