Although high pressure promotes alloying between hydrogen and iron, it has been believed that H/Fe is limited to 1 in the close-packed alloys. We report a substantial increase in the H solubility for iron through stabilization of superstoichiometric close-packed alloys promoted by Ni and high temperature. We also observe Fe-H polyhydrides at temperatures over 2500 K at high pressures, stability of which has been unknown at temperatures relevant for the planetary interiors. Considering recent results, large storage of H in the planetary cores is possible from H2-rich to even H2O-rich conditions. The H storage in the core can change the mass-radius relations where H has been assumed to de-gas to the atmosphere. Such H solubility and storage in the core are important to consider for understanding the “diluted core” of Jupiter, the “radius cliff” in the sub-Neptune exoplanets population, and massive exoplanets with very thin atmospheres.