We have measured the real space trajectory of the ultrafast magnetization dynamics in ferromagnetic metals induced by femtosecond optical pulses. Our approach allows the observation of the initial change of the modulus and orientation of the magnetization, occurring within a few hundreds of femtoseconds, as well as its subsequent precession and damping around the effective field. The role of the magnetocrystalline anisotropy shows up in the magnetization reorientation occurring during the electron-lattice relaxation. In addition, we propose a model which takes into account the initial demagnetization in the Bloch formalism describing the magnetization dynamics.