The influence of magnetohydrodynamic (MHD) convection on the thickness of an electrochemically deposited copper layer along a vertical plane cathode is examined. A magnetic gradient field, that induces a Lorentz force, establishes a vortical motion of the electrolyte which can be oriented either antiparallel or parallel to the natural convection. For the latter case, we show both experimentally and numerically that a sufficiently strong Lorentz force levels the inhomogeneities of the deposit thickness characteristic for deposition under pure natural convection.