Osmium tetroxide is reduced by molecular hydrogen in the presence of ligands in both polar and nonpolar solvents. In CHCl3 containing pyridine (py) or 1,10-phenanthroline (phen), OsO4 is reduced by H-2 to the known Os(VI) dimers L2Os(O)(2)(mu-O)(2)Os(O)(2)L-2 (L-2 = py(2), phen). However, in the absence of ligands in CHCl3 and other nonpolar solvents, OsO4 is unreactive toward H-2 over a week at ambient temperatures. In basic aqueous media, H-2 reduces OsO4(OH)(n)(n-) (n = 0, 1, 2) to the isolable Os(VI) complex, OsO2(OH)(4)(2-), at rates close to that found in py/CHCl3. Depending on the pH, the aqueous reactions are exergonic by Delta G = -20 to -27 kcal mol(-1), based on electrochemical data. The second-order rate constants for the aqueous reactions are larger as the number of coordinated hydroxide ligands increases, k(OsO4) = 1.6(2) x 10(-2) M-1 s(-1) k(OsO4(OH)-) = 3.8(4) x 10(-2) M-1 s(-1) < k(Oso4(OH)2)(2-) = 3.8(4) x 10(-1) M-1 s(-1). The observation of primary deuterium kinetic isotope effects, k(H2)/k(D2) = 3.1(3) for OsO4 and 3.6(4) for OsO4(OH)(-), indicates that the rate-determining step in each case involves H-H bond cleavage. Density functional calculations and thermochemical arguments favor a concerted [3+2] addition of H-2 across two oxo groups of OsO4(L)(n) and argue against H center dot or H- abstraction from H-2 or [2+2] addition of H-2 across one Os=O bond. The [3+2] mechanism is analogous to that of alkene addition to OsO4(L)(n) to form diolates, for which acceleration by added ligands has been extensively documented. The observation that ligands also accelerate H-2 addition to OsO4(L)(n) highlights the analogy between these two reactions.