We report the formation of a novel ferromagnetic state in the antiferromagnet BiFeO3 at the interface with ferromagnet La(0.7)Sr(0.3)MnO3. Using x-ray magnetic circular dichroism at Mn and Fe L(2,3) edges, we discovered that the development of this ferromagnetic spin structure is strongly associated with the onset of a significant exchange bias. Our results demonstrate that the magnetic state is directly related to an electronic orbital reconstruction at the interface, which is supported by the linearly polarized x-ray absorption measurement at the oxygen K edge.