A combination of experiments and numerical modeling was used to study the spatial evolution of the ferromagnetic phase transition in a thin film engineered to have a smooth gradient in exchange strength. Mean-field simulations predict, and experiments confirm, that a 100 nm Ni_{x}Cu_{1-x} alloy film with Ni concentration that varies by 9% as a function of depth behaves predominantly as if composed of a continuum of uncoupled ferromagnetic layers with continuously varying Curie temperatures. A mobile boundary separating ordered and disordered regions emerges as the temperature is increased. We demonstrate continuous control of the boundary position with temperature, and reversible control of the magnetization on both sides of the boundary with the magnetic field.