Trimethylamine N-oxide (TMAO) is a protecting osmolyte that stabilizes proteins against both temperature and pressure denaturation. Yet, even the solvation of TMAO itself is not well understood beyond ambient conditions. Here, using ab initio molecular dynamics, we analyze how its solvation structure changes upon compressing its ≈0.5 M aqueous solution from 1 bar to 10 kbar. The neat solvent, liquid water compressed to 10 kbar, is analyzed in detail to provide a meaningful gauge for the pressure-induced solvation changes of the solute. Pure water is shown to prefer to keep four H-bonded water molecules in a locally tetrahedral arrangement up to 10 kbar. The eye-catching shape changes of its oxygen-oxygen radial distribution function, where apparently the entire second peak is shifted into the first one, are traced back to about two more water molecules which are squeezed into the tetrahedral voids that are formed in the first shell by the H-bonded water molecules. These additional molecules increase the coordination number of pure water at 10 kbar significantly, but they are definitely not H-bonded to the central water molecule; rather they are its topological second to fourth H-bonded neighbors. The pressure response of TMAO(aq) is distinctly different, although its radial distribution functions do not change much. Under ambient conditions, the negatively charged oxygen site of the solute, which is strongly hydrophilic, predominantly accepts three H-bonds, whereas a roughly equal population of threefold and square-planar fourfold H-bonding is observed at 10 kbar. Moreover, only a negligible contribution of non-H-bonded water molecules is found in the first-shell region of TMAO even at 10 kbar, in contrast to the pressure response of water itself. In the hydrophobic region of TMAO, the solvating water molecules are found to straddle the three methyl groups at ambient pressure, which remains virtually unchanged upon compressing the solution to 10 kbar. Here, the pressure response is an increase from about 17 to 21 water molecules that solvate the methyl groups despite a sizable radial compression of the hydrophobic solvation shell.