  We present detailed forecasts for the constraints on primordial magnetic
fields (PMFs) that will be obtained with the LiteBIRD satellite. The
constraints are driven by the effects of PMFs on the CMB anisotropies: the
gravitational effects of magnetically-induced perturbations; the effects on the
thermal and ionization history of the Universe; the Faraday rotation imprint on
the CMB polarization; and the non-Gaussianities induced in polarization
anisotropies. LiteBIRD represents a sensitive probe for PMFs and by exploiting
all the physical effects, it will be able to improve the current limit coming
from Planck. In particular, thanks to its accurate $B$-mode polarization
measurement, LiteBIRD will improve the constraints on infrared configurations
for the gravitational effect, giving $B_{\rm 1\,Mpc}^{n_{\rm B} =-2.9} < 0.8$
nG at 95% C.L., potentially opening the possibility to detect nanogauss fields
with high significance. We also observe a significant improvement in the limits
when marginalized over the spectral index, $B_{1\,{\rm Mpc}}^{\rm marg}< 2.2$
nG at 95% C.L. From the thermal history effect, which relies mainly on $E$-mode
polarization data, we obtain a significant improvement for all PMF
configurations, with the marginalized case, $\sqrt{\langle B^2\rangle}^{\rm
marg}<0.50$ nG at 95% C.L. Faraday rotation constraints will take advantage of
the wide frequency coverage of LiteBIRD and the high sensitivity in $B$ modes,
improving the limits by orders of magnitude with respect to current results,
$B_{1\,{\rm Mpc}}^{n_{\rm B} =-2.9} < 3.2$ nG at 95% C.L. Finally,
non-Gaussianities of the $B$-mode polarization can probe PMFs at the level of 1
nG, again significantly improving the current bounds from Planck. Altogether
our forecasts represent a broad collection of complementary probes, providing
conservative limits on PMF characteristics that will be achieved with LiteBIRD.
