  The magnetic hyperfine (MHF) structure of the $5/2^+$(0.0 eV) ground state
and the low-lying $3/2^+$(7.8 eV) isomeric state of the $^{229}$Th nucleus in
highly charged ions Th$^{89+}$ and Th$^{87+}$ is calculated. The distribution
of the nuclear magnetization (the Bohr-Weisskopf effect) is accounted for in
the framework of the collective nuclear model with the wave functions of the
Nilsson model for the unpaired neutron. The deviations of the MHF structure for
the ground and isomeric states from their values in the model of point-like
nuclear magnetic dipole are calculated. The influence of the mixing of the
states with the same quantum number $F$ on the energy of sublevels is studied.
Taking into account the mixing of states, the probabilities of the transitions
between the components of MHF structure are found.
