Multimode optical fibres are enjoying renewed attention, boosted by the urgent need to overcome the current capacity crunch of single-mode fibre (SMF) systems and by recent advances in multimode complex nonlinear optics. In this work, we demonstrate that standard multimode fibres (MMFs) can be used as ultrafast all-optical tools for the transverse beam manipulation of high-power laser pulses. Our experimental data show that the Kerr effect in a graded-index (GRIN) MMF is the driving mechanism that overcomes speckle distortions, and leads to a counterintuitive effect that results in a spatially clean output beam robust against fibre bending. Our observations demonstrate that nonlinear beam reshaping into the fundamental mode of a MMF can be achieved even in the absence of a dissipative process such as stimulated scattering (Raman or Brillouin).