The solubility limit of elements plays a crucial role in alloy designing, as well as in the understanding of kinetic processes in alloys. Using first-principles calculations, we calculated the ground states of Fe-RE compound, and predicted the stable and metastable structures of Fe-Y and Fe-Ce. The results indicate that the stable structures for Fe-Y compounds are Fe₁₂Y.tI26, Fe₁₇Y₂.hP38 and Fe₂Y.cF24, and those for Fe-Ce binary are Fe₁₇Ce₂.hP38, Fe₁₉Ce₅.hR24 and Fe₂Ce.cF24. Based on the statistical-thermodynamic theory of dilute lattice gas, we presented a systematic series of calculations of the solubility limits of RE in α-Fe as a function of temperature. It is found that the solubilities are sorted in the following order: S_La>S_Ce>S_Y, correspond to the trend in the solubility formation enthalpies: H_sol(La)< H_sol(Ce)< H_sol(Y).