Experimental distribution coefficients of rare earth elements (REEs) between Fe oxyhydroxides (FeOOH) and Mn dioxide (δ-MnO2) and solutions [KD(REE)] exhibit anomalous variations: preferential uptake of light REEs by Mn dioxide, a step-like trend in KD(REE) in the Er-Tm-Yb-Lu region, and fractionation of KD(Y) from KD(Ho). Extended X-ray absorption fine structure (EXAFS) spectroscopy was applied to determine coordination states of Er, Tm, Yb, Lu, and Y adsorbed onto FeOOH and δ-MnO2 to assess structural changes around the REE site. The structures obtained, combined with previously determined structures of light REEs-sorbed Fe and Mn samples, corresponded to variations found in KD(REE). The structural parameters in the first coordination sphere suggest that La, Pr, and Nd adsorbed onto δ-MnO2 have a distorted tenfold-coordination sphere and differ greatly from La-, Pr-, Nd-, and Sm-sorbed FeOOH, which have a mixture of eightfold- and ninefold-coordination spheres. In contrast, heavy REEs including Y adsorbed onto Fe and Mn samples’ local structures have an eightfold-coordination sphere. The preferential uptakes of light REEs by δ-MnO2 are explained by the structural change. The irregular variations of heavy REEs and Y fractionation from Ho in KD(REE) do not, however, correspond to any change found in the coordination sphere. During characterization of the first coordination sphere, the W-type tetrad effect appears in the series variation of interatomic distances of REEaq3+ and REE-sorbed FeOOH and δ-MnO2. The occurrence of a tetrad effect indicates that the interatomic distances relate not only to the electrostatic field but also to a quantum field.