Self-assembled BiFeO3-CoFe2O4 nanocomposites were templated into ordered structures in which the ferrimagnetic CoFe2O4 pillars form square arrays of periods 60-100 nm in a ferroelectric BiFeO3 matrix. The ferroelectricity, magnetism, conductivity, and magnetoelectric coupling of the ordered nanocomposites were characterized by scanning probe microscopy. The insulating BiFeO3 matrix exhibited ferroelectric domains, whereas the resistive CoFe2O4 pillars exhibited single-domain magnetic contrast with high anisotropy due to the magnetoelasticity of the spinel phase. Magnetoelectric coupling was observed in which an applied voltage led to reversal of the magnetic pillars.