Short-lived proteins are degraded by proteasome complexes, which contain a proteolytic core particle (CP) but differ in the number of regulatory particles (RPs) and activators. A recently described member of conserved proteasome activators is Blm10. Blm10 contains 32 HEAT-like modules and is structurally related to the nuclear import receptor importin/karyopherin β. In proliferating yeast, RP-CP assemblies are primarily nuclear and promote cell division. During quiescence, RP-CP assemblies dissociate and CP and RP are sequestered into motile cytosolic proteasome storage granuli (PSG). Here, we show that CP sequestration into PSG depends on Blm10, whereas RP sequestration into PSG is independent of Blm10. PSG rapidly clear upon the resumption of cell proliferation and proteasomes are relocated into the nucleus. Thereby, Blm10 facilitates nuclear import of CP. Blm10-bound CP serves as an import receptor-cargo complex, as Blm10 mediates the interaction with FG-rich nucleoporins and is dissociated from the CP by Ran-GTP. Thus, Blm10 represents the first CP-dedicated nuclear import receptor in yeast.