  We compute the covariant Wigner function for spin-1/2 fermions in an
arbitrarily strong magnetic field by exactly solving the Dirac equation at
non-zero fermion-number and chiral-charge densities. The Landau energy levels
as well as a set of orthonormal eigenfunctions are found as solutions of the
Dirac equation. With these orthonormal eigenfunctions we construct the fermion
field operators and the corresponding Wigner-function operator. The Wigner
function is obtained by taking the ensemble average of the Wigner-function
operator in global thermodynamical equilibrium, i.e., at constant temperature
$T$ and non-zero fermion-number and chiral-charge chemical potentials $\mu$ and
$\mu_5$, respectively. Extracting the vector and axial-vector components of the
Wigner function, we reproduce the currents of the chiral magnetic and
separation effect in an arbitrarily strong magnetic field.
