Observation of high-temperature superconductivity in compressed sulfur hydrides has generated an irresistible wave of searches for new hydrogen-containing superconductors. We herein report the prediction of high-T_{c} superconductivity in tellurium hydrides stabilized at megabar pressures identified by first-principles calculations in combination with a swarm structure search. Although tellurium is isoelectronic to sulfur or selenium, its heavier atomic mass and weaker electronegativity makes tellurium hydrides fundamentally distinct from sulfur or selenium hydrides in stoichiometries, structures, and chemical bondings. We identify three metallic stoichiometries of H_{4}Te, H_{5}Te_{2}, and HTe_{3}, which are not predicted or known stable structures for sulfur or selenium hydrides. The two hydrogen-rich H_{4}Te and H_{5}Te_{2} phases are primarily ionic and contain exotic quasimolecular H_{2} and linear H_{3} units, respectively. Their high-T_{c} (e.g., 104 K for H_{4}Te at 170 GPa) superconductivity originates from the strong electron-phonon couplings associated with intermediate-frequency H-derived wagging and bending modes, a superconducting mechanism which differs substantially with those in sulfur or selenium hydrides where the high-frequency H-stretching vibrations make considerable contributions.