The precise control of nanostructure and surface atomic arrangement can be used to tune the electrocatalytic properties of materials and improve their performance. Unfortunately, the long-term structural stability of electrocatalysts with complex nanoscale morphology, a necessary requirement for industrial implementation, often remains elusive. Here we study how electrochemical and complex current behaviours affect the nanoscale object and its structural stability during electrocatalysis. We find that metal electromigration can drive structural transformation during electrolysis to minimize current crowding in nanoscale geometric constrictions. This electrical phenomenon, acting in combination with electrochemically induced atomic migration, can result in specific structural transformations of the catalyst, with the extent and rate depending on the material, geometry and reaction. Using a series of nanostructure examples, we establish a general framework for evaluating the structural transformations in cathodic metal nanocatalysts and explain specific qualitative trends. In conjunction with catalyst design rules, this mechanistic framework will facilitate the development of nanostructured electrocatalysts with sufficient stability for sustainable applications.