The NMR chemical shifts of hydride and fluoride ions in the solution phase are evaluated from the first principle. The cluster structure in the first solvation shell is calculated by density functional theory and MP2 theory, and the solvent effect around the cluster is considered by PCM and RISM-SCF-SEDD methods. The obtained shifts are analyzed in terms of electronic structure and solvent effects and are compared with available experimental data. The fluoride ion is deshielded in the presence of solvent molecules compared to the isolated state due to a larger paramagnetic contribution from the 2p orbital. On the other hand, there is no such change for the hydride ion. The paramagnetic and diamagnetic contributions are slightly changed due to the solvation, but they are canceled out. As a result, the chemical shift of the hydride ion is less affected by the solvent than that of the fluoride ion. The increased diamagnetic contribution of hydride ion dissolved in the solvent is attributed to the change in electron density coupled with microscopic solvation.