Activity of Piton de la Fournaise (PdF) volcano in La Réunion Island modifies the seismic velocities within the edifice. Using the 2010 and 2011 data from a network of 21 seismic stations in the vicinity of PdF, changes of seismic velocities are investigated using passive image interferometry, i.e. interferometry of seismic noise correlations. As noise correlations change significantly over time in response to volcanic activity, a method is presented that allows us to measure continuous long term velocity changes with high and constant accuracy by using multiple periods as reference. A long term velocity increase is found that averages about 0.25% per year. This trend is superimposed by short term changes that exhibit a clear connection with summit seismo-tectonic earthquakes indicating the effect of volcanic activity. Characteristic signatures of velocity changes are identified for post-eruptive periods of deflation that show an increase of velocity associated with subsidence observed by GPS. Periods of pre-eruptive inflation are characterized by decreasing velocity. Seismic crises can be associated with either increasing or decreasing velocity depending on whether the magma movement leads to deflation due to an eruption emptying the shallow plumbing system or to inflation caused by a non-eruptive intrusion. With a simple assumption about the spatial sensitivity of the measurements both processes are found to have the strongest effect in the central summit area of the volcano which also shows the strongest surface displacements during the time investigated here. We do not observe a dependence of the velocity change on the location of the erupting fissures, instead the distribution of changes for the three inflation periods and the two eruptions are similar indicating that the velocity changes observed here reflect the dynamics of a shallow magma reservoir rather than the effect of the eruption at the surface.