  White dwarfs (WDs) and neutron stars (NSs) are among the most magnetized
astrophysical objects in the universe, with magnetic fields that can reach up
to $10^9\,\mathrm{G}$ for WDs and up to $10^{15}\,\mathrm{G}$ for NSs. The
galaxy is expected to be populated with approximately one hundred million of
double WD and millions of NS-WD binaries. Throughout the duration of the
mission, the Laser Interferometer Space Antenna (LISA) will observe
gravitational waves (GWs) emitted simultaneously by more than ten thousand of
such galactic binaries. In this paper, we investigate the effect of the
magnetic dipole-dipole interaction on the GW signal emitted by magnetic
galactic binaries. We derive the secular equations governing the orbital and
rotational motion of these objects. Then, we integrate these equations both
numerically and analytically. We conclude that the overall visible effect is an
additional secular drift of the mean longitude. This drift is proportional to
the product of the magnetic moments and is inversely proportional to the $7/2$
power of the semi-major axis. Finally, we show that, at zeroth-order in
eccentricity, the magnetic dipole-dipole interaction shifts the main frequency
of the gravitational strain measured by LISA.
