Development of functional polymer-grafted nanoparticles for various nanotechnological applications, including nanomedicine, requires understanding of the interplay of design parameters governed by the underlying polymer physics principles. Using atomistic molecular dynamics simulation, we investigate hydration and structural properties of spherical gold nanoparticles (1 and 3 nm in radius) with grafted polyethylene oxide (PEO) of different lengths at two grafting densities. We demonstrate that the criterion for planar surfaces is insufficient to achieve the brush regime for nanoparticles of high curvature as the chain conformation and hydration remain very similar to aqueous solution, thereby exposing the nanoparticle surface, which may compromise the stealth properties of PEO-grafted nanoparticles. A new criterion for achieving the brush regime is proposed, accounting for nanoparticle curvature. At high grafting density (4.2 nm(-2)), we find that the PEO brush is rather dense and partially dehydrated in the vicinity of the gold nanoparticle surface, in agreement with experimental observations. In contrast to experimental assumptions and some analytical predictions, we find that polymer density decreases with radial distance as r(-4/3) throughout the brush including the dense region, where PEO chains are stretched and oriented independent of PEO length. Chain stretching and orientation lead to an N-4/5 scaling dependence for the brush height, which is stronger than classical theoretical predictions but agrees with reported experimental data. PEO tail flexibility, which is relevant for inhibition of protein adsorption, is found to increase substantially with chain length and distance from the nanoparticle core.