Epitaxial Co40Fe40B20 and Co55Fe45 (further-CoFe(B)) films were grown on Bi2Te3(0001) and Bi2Se3(0001) substrates by the laser molecular beam epitaxy (LMBE) technique at 200-400 °C. Structurally ordered ferromagnetic thin films were obtained on topological insulator surfaces for the first time. A body-centered cubic-type (bcc) crystalline structure of CoFe(B) with the (111) plane parallel to the (0001) plane of Bi2Te3 was observed, in contrast to the polycrystalline CoFe(B) film formed on Bi2Se3(0001) at RT using a high-temperature seeding layer. Using RHEED 3D reciprocal space mapping, the epitaxial relationships for the CoFe(B)/Bi2Te3 heterostructure were revealed. MOKE and AFM measurements showed the isotropic azimuthal in-plane behavior of the magnetization vector in CoFe(B)/Bi2Te3, in contrast to uniaxial magnetic anisotropy observed in CoFe(B)/Bi2Se3. XPS measurements showed a higher stability of CoFe(B) grown on Bi2Te3 towards oxidation, compared to that of CoFe(B) grown on Bi2Se3. XAS and XMCD measurements for both types of concerned nanostructures allowed the calculation of spin and orbital magnetic moments for Co and Fe. Additionally, we have studied the crystalline structure and magnetic properties of the CoFe(B)/BiTeI system with giant Rashba splitting.