Context. Searches for exoplanets with radial velocity techniques are increasingly sensitive to stellar activity. It is therefore crucial to characterize how this activity influences radial velocity measurements in their study of the detectability of planets in these conditions. Aims. In a previous work we simulated the impact of spots and plages on the radial velocity of the Sun. Our objective is to compare this simulation with the observed radial velocity of the Sun for the same period. Methods. We use Dopplergrams and magnetograms obtained by MDI/SOHO over one solar cycle to reconstruct the solar integrated radial velocity in the Ni line 6768 Å. We also characterize the relation between the velocity and the local magnetic field to interpret our results. Results. We obtain a stronger redshift in places where the local magnetic field is larger (and as a consequence for larger magnetic structures): hence we find a higher attenuation of the convective blueshift in plages than in the network. Our results are compatible with an attenuation of this blueshift by about 50% when averaged over plages and network. We obtain an integrated radial velocity with an amplitude over the solar cycle of about 8 m s-1, with small-scale variations similar to the results of the simulation, once they are scaled to the Ni line. Conclusions. The observed solar integrated radial velocity agrees with the result of the simulation made in our previous work within 30%, which validates this simulation. The observed amplitude confirms that the impact of the convective blueshift attenuation in magnetic regions will be critical to detect Earth-mass planets in the habitable zone around solar-like stars.