The low-energy effective description of Weyl semimetals is defined by the axion electrodynamics, which captures the effects arising due to the presence of nodes of opposite chirality in the electronic structure. Here, we explore the magnetoelectric response of time-reversal breaking (TRB) Weyl superconductors in the London regime. The influence of the axion contribution leads to an increase in the London penetration depth—a behavior that can be anticipated by first considering the photon spectrum of a TRBWeyl semimetal.Moreover, we find that both the Meissner state and the vortex phase feature an interplay between the electric and magnetic fields. This leads to a nonvanishing electromagnetic angular momentum, which we calculate for a number of geometrical configurations.