We use the three-flavor Nambu--Jona-Lasinio model, which includes strangeness and quark physical masses in the mean field approximation, to investigate the influence of strong magnetic fields on the QCD phase diagram covering the whole $T-��$ plane. It is found that the size of the first order transition line increases as the field strength increases so that a larger coexistence region for hadronic and quark matter should be expected for strong magnetic fields. The location of the critical end point is also affected by the presence of magnetic fields which invariably increase the temperature value at which the first order line terminates. On the other hand, the critical end point chemical potential value displays a subtle oscillation around the B=0 value for magnetic fields within the $10^{17}-10^{20} \, {\rm G}$ range. These findings may have non trivial consequences for the physics of magnetars and heavy ion collisions.

5 pages, 2 figures