Phosphogypsum (CaSO4·2H2O, PG) waste is produced in large amounts during phosphoric acid (H3PO4) production. Minor quantities are utilized in construction or agriculture, while most of the material is stockpiled, creating an environmental challenge to prevent pollution of natural waters. In principle, the gypsum waste could be used to capture several hundred megatonnes of carbon dioxide (CO2). For example, when gypsum is converted to ammonium sulfate [(NH4)2SO4] with ammonia (NH3) and CO2, also solid calcium carbonate (CaCO3) is generated. The ammonium sulfate can be utilized as a fertilizer or in other mineral carbonation processes that use magnesium silicate-based rock as feedstock, while calcium carbonate has various uses as, e.g., filler material. The reaction extent of the described process was studied by thermodynamic modeling and experimentally as a function of reactant concentrations and temperature. Other essential properties such as purity and quality of the solid products are also followed. Conversion efficiencies of >95% calcium from PG to calcium carbonate are obtained. Scalenohedral, rhombohedral, and prismatic calcite particles can be produced, although the precipitates contain certain contaminants such as rare earth metals and sulfur from the gypsum. A reverse osmosis membrane cartridge is also tested as an alternative and energy-efficient method of concentrating the ammonium sulfate salt solution instead of the traditional evaporation of the process solution.