The adsorption of radioactive iodate (IO₃⁻) and iodide (I⁻) anions on natural minerals is critical for nuclear environmental safety. Allophane, a nanosized clay mineral, is considered to adsorb IO₃⁻ and I⁻, but the essential interactions between both anions and allophane remain unknown, due to the challenges of characterizing extremely small allophane nanoparticles in complex soils and obtaining high-purity natural allophane. In this work, neat allophane (Allo) nanoparticles were synthesized and used to study their adsorption for IO₃⁻ and I⁻ anions. The adsorption kinetics, adsorption thermodynamics, pH-dependent adsorption-desorption, and competitive adsorption (Cl⁻ and SO₄²⁻) were quantitatively investigated. Moreover, combined with advanced spectroscopic analyses of X-ray absorption fine structure (XAFS) and X-ray photoelectron spectroscopy (XPS), the atomistic adsorption mechanisms were illustrated. The adsorption capacities of Allo can be about 0.22 mmol/g for IO₃⁻ and 0.077 mmol/g for I⁻, which are at least one order of magnitude and 2.6-fold higher than those of other clay minerals, respectively. The IO₃⁻ adsorption involved the ligand exchange and electrostatic attraction interactions, while the I⁻ adsorption involved the Lewis acid-base and hydrogen-bond interactions. The inner-sphere adsorption mainly occurred in the wedge-shaped nanopores within Allo. The findings will improve the understanding of IO₃⁻ and I⁻ adsorption on allophane, promote the practical applications of natural allophane in the management of nuclear wastes, and provide foundations for revealing the geochemical behaviors of iodine.