We calculate shot noise and the corresponding Fano factors in magnetic double-barrier tunnel junctions. Two situations are analyzed: (i) the central metallic layer is nonmagnetic while the external ones are ferromagnetic, and (ii) all of the metallic layers are ferromagnetic. In the latter case, the number of various magnetic configurations of the junctions is larger, which improves the functionality of such devices. The corresponding shot noise and Fano factor are shown to depend on the magnetic configuration of the junctions. The effect of spin relaxation in the central layer is also taken into account. The theoretical results are compared with experimental data on the shot noise in Fe/MgO/Fe/MgO/Fe structures.