We study the condensation phenomenon for a system of charged bosons in the presence of an external magnetic field. We show that condensation happens for a definite critical temperature instead of through a diffuse phase transition. The essential ingredient, overlooked in previous analyses and accounted for in this work, is the treatment of the plasma screening effects by means of resummation. We compute the critical temperature, for the case in which the condensate is made of charged pions and for typical densities found in compact astrophysical objects, for small and large values of the magnetic field. We show that the magnetic field catalyzes the onset of condensation at very small and at large values of the magnetic field, and that for intermediate values the critical temperature for condensation is lower than for the zero magnetic field case.