The structure and properties of the Fe8O12Hn clusters (n = 0-18) are computed using the all-electron density functional theory with the generalized gradient approximation for the exchange-correlation potential. The ground state of Fe8O12 is found to be a singlet state having a bi-capped octahedron geometry. Upon hydrogenation, the octahedral framework of Fe is retained in Fe8O12Hn up to n < 7, beyond which point the iron octahedron transforms into a cube. Hydrogen atoms are bound to oxygen atoms up to n = 12, but they bind to the faces of the Fe8 cube when n > 12. The total spin magnetic moment of a Fe8O12Hn cluster is larger than 6 μB for 1 ≤ n ≤ 18, except for n = 8 and 10, where the lowest total energy states are antiferromagnetic singlets. The reason for this deviation from the general behavior in the Fe8O12Hn series is attributed to the collective superexchange phenomenon. Surprisingly, the total spin magnetic moment of a Fe8O12Hn cluster is found to be substantially larger than the total spin magnetic moment of the bare Fe8 cluster when n = 12-18. All of the Fe8O12Hn clusters are stable with respect to an abstraction of a single hydrogen atom but are unstable toward the abstraction of an H2 dimer when n =10 and n = 14-18.