  Non-centrosymmetric superconductors exhibit the magnetoelectric effect which
manifests itself in the appearance of the magnetic spin polarization in
response to a dissipationless electric current (supercurrent). While much
attention has been dedicated to the thermodynamic version of this phenomenon
(Edelstein effect), non-equilibrium transport magnetoelectric effects have not
been explored yet. We propose the magnetoelectric Andreev effect (MAE) which
consists in the generation of spin-polarized triplet Andreev conductance by an
electric supercurrent. The MAE stems from the spin polarization of the
Cooper-pair condensate due to a supercurrent-induced non-unitary triplet
pairing. We propose the realization of such non-unitary pairing and MAE in
superconducting proximity structures based on two-dimensional helical metals --
strongly spin-orbit-coupled electronic systems with the Dirac spectrum such as
the topological surface states. Our results uncover an unexplored route towards
electrically controlled superconducting spintronics and are a smoking gun for
induced unconventional superconductivity in spin-orbit-coupled materials.
