We report the first experimental observation of negatively charged hydrogen and deuterium cluster ions, H_{n}^{-} and D_{n}^{-}, where n≥5. These anions are formed by an electron addition to liquid helium nanodroplets doped with molecular hydrogen or deuterium. The ions are stable for at least the lifetime of the experiment, which is several tens of microseconds. Only anions with odd values of n are detected, and some specific ions show anomalously high abundances. The sizes of these "magic number" ions suggest an icosahedral framework of H_{2} (D_{2}) molecules in solvent shells around a central H^{-} (D^{-}) ion. The first three shells, which contain a total of 44 H_{2} or D_{2} molecules, appear to be solidlike, but thereafter a more liquidlike arrangement of the H_{2} (D_{2}) molecules is adopted.