Migration of boron in CoFeB/MgO multilayer during amorphous to crystalline transformation in CoFeB has been studied using Polarized Neutron Reflectivity (PNR) and anomalous Soft X-ray Reflectivity (SXR). PNR gives information about the possible redistribution of B in the multilayer during thermal annealing, as well as about the variation in the average magnetic moment. Sensitivity of the soft X-ray reflectivity to the movement of boron is enhanced by doing a series of measurements with X-ray energy spanning across the K absorption edge of B. Both the PNR and anomalous SXR results clearly suggest that upon thermal annealing, boron prefers to move away from the MgO/CoFeB interfaces, and forms a layer of boride in the middle of the magnetic layer. These results are important in view of the existing ambiguity regarding the role of boron in CoFeB/MgO based magnetic tunnel junctions.