The use of waste to capture CO2 has been on the rise, to reduce costs and to improve the environmental footprint. Here, a flue gas desulfurization (FGD) gypsum waste is proposed, which allows us to obtain a CaCO3-based solid, which should be recycled. The CO2 capture stage has primarily been carried out via the direct carbonation method or at high temperature. However, a high energy penalty and/or long reaction times make it unattractive from an industrial perspective. To avoid this, herein an indirect method is proposed, based on first capturing the CO2 with NaOH and later using an aqueous carbonation stage. This allows us to capture CO2 at a near-ambient temperature, improving reaction times and avoiding the energy penalty. The parameters studied were Ca2+/CO32− ratio, L/S ratio and temperature. Each of them has been optimized, with 1.25, 100 mL/g and 25 °C being the optimal values, respectively, reaching an efficiency of 72.52%. Furthermore, the utilization of the produced CaCO3 as a building material has been analyzed. The density, superficial hardness and the compressive strength of a material composed of 10 wt% of CaCO3 and 90 wt% of commercial gypsum, with a water/solid ratio of 0.5, is measured. When the waste is added, the density and the mechanical properties decreased, although the compressive strength and superficial hardness are higher than the requirements for gypsum panels. Thus, this work is promising for the carbonation of FGD-gypsum, which involves its chemical transformation into calcium carbonate through reacting it with the CO2 of flue gasses and recycling the generated wastes in construction materials.