The present paper demonstrates the feasibility of X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) under high magnetic fields up to 26 T and low temperatures down to 5 K on the ID24 energy-dispersive XAS beamline of the ESRF. The pulsed magnetic field set-up, entirely developed at the ESRF, is described as well as the beamline set-up, the synchronization and the measurement procedure. It allows field strengths up to 30 T. Finally, as an example, we report a recent XMCD study at the Re L2 and L3 absorption edges of the double perovskite Sr2CrReO(6).