The research on the functional properties of medium- and high-entropy alloys (MEAs and HEAs) has been in the spotlight recently. Many significant discoveries have been made lately in hydrogen-based economy-related research where these alloys may be utilized in all of its key sectors: water electrolysis, hydrogen storage, and fuel cell applications. Despite the rapid development of MEAs and HEAs with the ability to reversibly absorb hydrogen, the research is limited to transition-metal-based alloys that crystallize in body-centered cubic solid solution or Laves phase structures. To date, no study has been devoted to the hydrogenation of rare-earth-element (REE)-based MEAs or HEAs, as well as to the alloys crystallizing in face-centered-cubic (FCC) or hexagonal-close-packed structures. Here, we elucidate the formation and hydrogen storage properties of REE-based ScYNdGd MEA. More specifically, we present the astounding stabilization of the single-phase FCC structure induced by the hydrogen absorption process. Moreover, the measured unprecedented high storage capacity of 2.5 H/M has been observed after hydrogenation conducted under mild conditions that proceeded without any phase transformation in the material. The studied MEA can be facilely activated, even after a long passivation time. The results of complementary measurements showed that the hydrogen desorption process proceeds in two steps. In the first, hydrogen is released from octahedral interstitial sites at relatively low temperatures. In the second, high-temperature process, it is associated with the desorption of hydrogen atoms stored in tetrahedral sites. The presented results may impact future research of a novel group of REE-based MEAs and HEAs with adaptable hydrogen storage properties and a broad scope of possible applications.