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}=-0.35μ_{N} in surprisingly good agreement with the experimentally determined value of -0.37(6)μ_{N}, while overestimating the ground state dipole moment by a factor 1.4. The model provides further information on the role and strength of the Coriolis mixing and the most probable value of the gyromagnetic ratio g_{R} and its consequences for the transition probability B(M1). The key role of the magnetic moment values as constraints in the determination of the isomer decay rates is discussed.