Micro-structured copper layers are obtained from pulse-reverse electrodeposition on a planar gold electrode that is magnetically patterned by magnetized iron wires underneath. 3D numerical simulations of the electrodeposition based on an adapted reaction kinetics are able to nicely reproduce the micro-structure of the deposit layer, despite the height values still remain underestimated. It is shown that the structuring is enabled by the magnetic gradient force, which generates a local flow that supports deposition and hinders dissolution in the regions of high magnetic gradients. The Lorentz force originating from radial magnetic field components near the rim of the electrode causes a circumferential cell flow. The resulting secondary flow, however, is superseded by the local flow driven by the magnetic gradient force in the vicinity of the wires. Finally, the role of solutal buoyancy effects is discussed to better understand the limitations of structured growth in different modes of deposition and cell geometries.