Rare earth-bearing gypsum tailings from the fertilizer industry are a potential source for an economically viable and sustainable production of rare earth elements. Large quantities are generated inter alia in Catalão, Brazil, as a by-product in a fertilizer production plant. Hitherto, the gypsum has been used as soil conditioner in agriculture or was dumped. The cooperative project, “Catalão Monazite: Economical exploitation of rare earth elements from monazite-bearing secondary raw materials,” intends to extract rare earth elements from these gypsum tailings. In this paper, a chemical process route to obtain a mixed rare earth carbonate from a monazite concentrate, was investigated. The results of the digestion, leaching, and precipitation experiments are presented and discussed herein. This includes reagent choice, process parameter optimization through experimental design, mineralogical characterization of the feed material and residues, purification of the leach solution, and precipitation of the rare earth as carbonates. The results showed that a rare earth extraction of about 90% without the mobilization of key impurities is possible during a sulfuric acid digestion with two heating stages and subsequent leaching with water. In the following purification step, the remaining impurities were precipitated with ammonium solution and the rare earth elements were successfully recovered as carbonates with a mixture of ammonium solution and ammonium bicarbonate.