The present invention relates to a process for purifying and concentrating rare earths contained in phosphogypsum, characterised in that it comprises the following steps of: from a phosphogypsum, a) Leaching the phosphogypsum with a solution of one or more strong acid(s) selected from among: sulphuric acid, nitric acid and hydrochloric acid, in order to obtain a leaching mixture comprising a liquid phase formed by a leaching solution containing rare earths from the phosphogypsum and the leaching acid, and a solid phase comprising the phosphogypsum, b) Adding, to the phosphogypsum, an oxidising agent to promote passage of the rare earths from the phosphogypsum into the leaching solution, and/or a reducing agent to reduce solubility of mineral impurities contained in the leaching solution in order to allow their passage from the leaching solution into the solid phase, c) Separating the liquid phase enriched in rare earths and depleted in mineral impurities, and the solid phase enriched in mineral impurities.