Histones are synthesized and processed in the cytoplasm and then transported into the nucleus for assembly into nucleosomes. H2A-H2B is imported into the S. cerevisiae nucleus by the importin Kap114, which also imports the most prominent H2A-H2B chaperone, Nap1. We understand how Kap114 recognizes H2A-H2B for nuclear import, but little is known about how it recognizes Nap1. Furthermore, the ternary complex of Nap1, H2A-H2B and Kap114 was previously detected in both the cytosol and the nucleus, but its role in nuclear import is unclear. Here, we present biophysical analysis of interactions between Nap1, H2A-H2B, Kap114 and RanGTP, and cryo-electron microscopy structures of ternary Kap114, Nap1 and H2A-H2B complexes. Kap114 binds Nap1 very weakly, but H2A-H2B enhances Kap114-Nap1 interaction to form a ternary Kap114/Nap1/H2A-H2B complex that is stable in the absence and presence of RanGTP. Cryogenic electron microscopy structures reveal two distinct ternary Kap114/Nap1/H2A-H2B complexes: a 3.2 Å resolution structure of Nap1 bound to H2A-H2B-bound Kap114 where Nap1 does not contact H2A-H2B, and a 3.5 Å resolution structure of H2A-H2B sandwiched between Nap1 and Kap114. Collectively, these results lead to a mechanistic model of how Nap1·H2A-H2B encounters Kap114 in the cytoplasm and how both H2A-H2B and Nap1 are chaperoned and co-imported by Kap114 into the nucleus. The model also suggests how RanGTP-binding stabilizes a quaternary RanGTP/Kap114/Nap1/H2A-H2B complex that facilitates hand-off of H2A-H2B from Kap114 to Nap1, the assembling nucleosome or other nuclear chaperone.