Finite size effects on the ferroic orders in BiFeO3 are studied by atomic pair distribution function analysis and magnetic measurements. While bulk rhombohedral BiFeO3 exhibits ferroelectricity and antiferromagnetism with a cycloidal magnetic moment arrangement leading to zero magnetization and weak magnetoelectric coupling, BiFeO3 nanoparticles with a size smaller than the spin cycloid period of 62 nm preserve their polar rhombohedral structure and develop ferromagnetism, thus exhibiting coexisting polarization and nonzero magnetization that enhances the magnetoelectric coupling. When the nanoparticles become smaller than 17 nm, however, their crystal lattice expands and becomes nonpolar cubic. They also become superparamagnetic and thus simultaneously cease exhibiting both ferroelectricity and ferromagnetism. Our findings shed light on the interaction between the lattice structure and ferroic orders in nanophase perovskites and also provide a rare example of a lattice symmetry breaking phase transition that determines their critical size.