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Ferromagnet/ferroelectric interface materials have emerged as structures with strong magnetoelectric coupling that may exist due to unconventional physical mechanisms. Here we present a first-principles study of the magnetoelectric effect at the ferromagnet/ferroelectric SrRuO3 /BaTiO3 (001) interface. We find that the exchange splitting of the spin-polarized band structure, and therefore the magnetization, at the interface can be altered substantially by reversal of the ferroelectric polarization in the BaTiO3. These magnetoelectric effects originate from the screening of polarization charges at the SrRuO3 /BaTiO3 interface and are consistent with the Stoner model for itinerant magnetism.