Newly synthesised histones are thought to dimerise in the cytosol and undergo nuclear import in complex with histone chaperones. Here, we provide evidence that human H3.1 and H4 are imported into the nucleus as monomers. Using a tether-and-release system to study the import dynamics of newly synthesised histones, we find that cytosolic H3.1 and H4 can be maintained as stable monomeric units. Cytosolically tethered histones are bound to importin-alpha proteins (predominantly IPO4), but not to histone-specific chaperones NASP, ASF1a, RbAp46 (RBBP7) or HAT1, which reside in the nucleus in interphase cells. Release of monomeric histones from their cytosolic tether results in rapid nuclear translocation, IPO4 dissociation and incorporation into chromatin at sites of replication. Quantitative analysis of histones bound to individual chaperones reveals an excess of H3 specifically associated with sNASP, suggesting that NASP maintains a soluble, monomeric pool of H3 within the nucleus and may act as a nuclear receptor for newly imported histone. In summary, we propose that histones H3 and H4 are rapidly imported as monomeric units, forming heterodimers in the nucleus rather than the cytosol.