The soft magnetic properties in iron-based nanocrystalline alloys have generally been achieved through the addition of nonmagnetic additives, but this has the unwanted effect of reducing the saturation magnetization. In a recent advance, it was shown that magnetically soft nanostructured alloys could be prepared from a simple, binary Fe-B amorphous precursor by ultrarapid annealing (URA). These materials had a saturation magnetization comparable to that of silicon steel, while a refined grain structure resulted in considerably lower core losses through the exchange averaging effect of the magnetic anisotropy. As yet, the formation mechanism of the soft magnetic nanostructure in this simple binary system has not been identified. We investigated the crystallization process of amorphous Fe86B14 using in situ transport measurements. The relationship between the resistivity and the volume fraction of bcc-Fe crystallites was calibrated by 57Fe Mössbauer spectroscopy. In this paper, we show that the isothermal crystallization behavior of these Fe-B amorphous alloys is well described by the Johnson-Mehl-Avrami-Kolmogorov kinetic model and that the the Avrami exponent (n) shows a tendency to increase with increasing annealing temperature (Ta); the exponent n is approximately 1.5 at Ta<700K while n>2 at Ta=729K. This suggests that below 700 K the nucleation rate is governed solely by a limited number of quenched-in nuclei whereas at higher temperatures, homogeneous nucleation starts to dominate. Since the onset of crystallization is increased dramatically by rapid heating, the formation of the refined nanostructure induced by URA can be well understood by an increase in the number density of nuclei due to homogeneous nucleation. The increased homogeneous nucleation at higher annealing temperatures can be linked to enhanced atomic transport due to viscous flow.