We have investigated the hyperfine structure of the transition between the 5d{7}6s{2} {4}F{9/2}{e} ground state and the 5d{6}6s{2}6p {6}D{J}{o} excited state in the negative osmium ion by high-resolution collinear laser spectroscopy. This transition is unique because it is the only known electric-dipole transition in atomic anions and might be amenable to laser cooling. From the observed hyperfine structure in 187Os- and 189Os- the yet unknown total angular momentum of the bound excited state was found to be J=9/2. The hyperfine structure constants of the {4}F{9/2}{e} ground state and the {6}D{9/2}{o} excited state were determined experimentally and compared to multiconfiguration Dirac-Fock calculations. Using the knowledge of the ground and excited state angular momenta, the full energy level diagram of 192Os- in an external magnetic field was calculated, revealing possible laser cooling transitions.