The diffusion of colloidal nanoparticles and nanomolecular aggregates, which plays an important role in various biophysical and physicochemical phenomena, is currently under intense study. Here, we examine the shape and size dependent diffusion of colloidal nano- particles, fused nanoclusters and nanoaggregates using a hybrid fluctuating lattice Boltzmann-Molecular Dynamics method. We use physically realistic parameters characteristic of an aqueous solution, with explicitly implemented microscopic no-slip and full-slip boundary conditions. Results from nanocolloids below 10 nm in radii demonstrate how the volume fraction of the hydrodynamic boundary layer influences diffusivities. Full-slip colloids are found to diffuse faster than no-slip particles. We also characterize the shape dependent anisotropy of the diffusion coefficients of nanoclusters through the Green-Kubo relation. Finally, we study the size dependence of the diffusion of nanoaggregates comprising N ≤ 108 monomers and demonstrate that the diffusion coefficient approaches the continuum scaling limit of N−1/3.