A recent laser spectroscopy experiment [J. Thielking et al., Nature, (London) 556, 321 (2018)] has determined for the first time the magnetic dipole moment of the 7.8 eV isomeric state 229m Th. The measured value differs by a factor of approximately 5 from previous nuclear theory predictions based on the Nilsson model, raising questions about our understanding of the underlying nuclear structure. Here, we present a new theoretical prediction based on a nuclear model with coupled collective quadrupole-octupole and single-particle motions. Our calculations yield an isomer magnetic dipole moment of µ IS = −0.35µN in surprisingly good agreement with the experimentally determined value of −0.37(6)µN , while overestimating the ground state dipole moment by a factor 1.4. The model provides further information on the states' parity mixing, the role and strength of the Coriolis mixing and the most probable value of the gyromagnetic ratio gR and its consequences for the transition probability B(M 1).