The invention relates to a process for the preparation of anhydrous magnesium sulfate or magnesium sulfate hydrates, wherein magnesium sulfite or magnesium hydrogen sulfite obtained from a flue gas desulfurization process is oxidized. According to the invention the magnesium sulfite or magnesium hydrogen sulfite is oxidized in a solid state or as a slurry, at elevated pressure and temperature, to magnesium sulfate having a gross formula of MgvSxHyOz, where v = 1-2, x = 1-2, y = 0-14, and z = 4-16.
