We measure the center-of-mass diffusion of silica nanoparticles (NPs) in entangled poly(2-vinylpyridine) (P2VP) melts using Rutherford backscattering spectrometry. While these NPs are well within the size regime where enhanced, nonhydrodynamic NP transport is theoretically predicted and has been observed experimentally (2R_NP/d_tube ≈ 3, where 2R_NP is the NP diameter and d_tube is the tube diameter), we find that the diffusion of these NPs in P2VP is in fact well-described by the hydrodynamic Stokes–Einstein relation. The effective NP diameter 2R_eff is significantly larger than 2R_NP and strongly dependent on P2VP molecular weight, consistent with the presence of a bound polymer layer on the NP surface with thickness h_eff ≈ 1.1R_g. Our results show that the bound polymer layer significantly augments the NP hydrodynamic size in polymer melts with attractive polymer–NP interactions and effectively transitions the mechanism of NP diffusion from the nonhydrodynamic to hydrodynamic regime, particularly at high molecular weights where NP transport is expected to be notably enhanced. Furthermore, these results provide the first experimental demonstration that hydrodynamic NP transport in polymer melts requires particles of size ≳5d_tube, consistent with recent theoretical predictions.