We investigate the compaction dynamics of vibrated granular suspensions using both digital imaging technique and MRI measurements. Starting from initialy loose packings, our experimental data suggest the existence of two stages in the compaction dynamics: a fast stage at short times where a rising compaction front propagates through the granular suspension and a slow stage at large times where the packing compacts slowly and homogeneously. The compaction dynamics in each stage can be well fitted to usual stretched exponential laws with stretching exponents equal to 2 and 0.45, respectively. The transition time between these two stages, tau(c), depends on the fluid viscosity, vibration intensity and grain diameter. We show that tau(-1)(c) and the velocity of the front decrease roughly linearly with the lubrication Peclet number, Pe(lub) related to the competition between the lubrication stress induced by vibrations and the granular pressure.