  In this paper, we prove global existence of solutions with analytic
regularity to the 2D MHD boundary layer equations in the mixed Prandtl and
Hartmann regime derived by formal multi-scale expansion in \cite{GP}. The
analysis shows that the combined effect of the magnetic diffusivity and
transveral magnetic field on the boundary leads to a linear damping on the
tangential velocity field near the boundary. And this damping effect yields the
global in time analytic norm estimate in the tangential space variable on the
perturbation of the classical steady Hartmann profile.
