Magnonics explores precessional excitations of ordered spins in magnetic materials - so-called spin waves - and their use as information and signal carriers within networks of magnonic waveguides. Here, we demonstrate that the nonuniformity of the internal magnetic field and magnetization inherent to magnetic structures creates a medium of graded refractive index for propagating magnetostatic waves and can be used to steer their propagation. The character of the nonuniformity can be tuned and potentially programmed using the applied magnetic field, which opens exciting prospects for the field of graded-index magnonics. © 2015 American Physical Society.